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  27.       <h1 class="title">std/complex</h1>
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  40.         <li><a href="manual.html">Manual</a></li>
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  41.         <li><a href="lib.html">Standard library</a></li>
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  42.         <li> <a id="indexLink" href="theindex.html">Index</a></li>
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  53.     <ul class="simple simple-toc" id="toc-list">
    54. 

  54.   <li>
    55. 

  55.   <a class="reference reference-toplevel" href="#6" id="56">Imports</a>
    56. 

  56. </li>
    57. 

  57. <li>
    58. 

  58.   <details open>
    59. 

  59.     <summary><a class="reference reference-toplevel" href="#7" id="57">Types</a></summary>
    60. 

  60.     <ul class="simple simple-toc-section">
    61. 

  61.       <li><a class="reference" href="#Complex" title="Complex[T] = object
    62. 

  62.   re*, im*: T">Complex</a></li>
    63. 

  63. <li><a class="reference" href="#Complex32" title="Complex32 = Complex[float32]">Complex32</a></li>
    64. 

  64. <li><a class="reference" href="#Complex64" title="Complex64 = Complex[float64]">Complex64</a></li>
    65. 

  65. 

  66.     </ul>
    67. 

  67.   </details>
    68. 

  68. </li>
    69. 

  69. <li>
    70. 

  70.   <details open>
    71. 

  71.     <summary><a class="reference reference-toplevel" href="#12" id="62">Procs</a></summary>
    72. 

  72.     <ul class="simple simple-toc-section">
    73. 

  73.       <ul class="simple nested-toc-section">$
    74. 

  74.   <li><a class="reference" href="#%24%2CComplex" title="`$`(z: Complex): string">`$`(z: Complex): string</a></li>
    75. 

  75. 

  76. </ul>
    77. 

  77. <ul class="simple nested-toc-section">*
    78. 

  78.   <li><a class="reference" href="#%2A%2CComplex%5BT%5D%2CComplex%5BT%5D" title="`*`[T](x, y: Complex[T]): Complex[T]">`*`[T](x, y: Complex[T]): Complex[T]</a></li>
    79. 

  79. <li><a class="reference" href="#%2A%2CComplex%5BT%5D%2CT" title="`*`[T](x: Complex[T]; y: T): Complex[T]">`*`[T](x: Complex[T]; y: T): Complex[T]</a></li>
    80. 

  80. <li><a class="reference" href="#%2A%2CT%2CComplex%5BT%5D" title="`*`[T](x: T; y: Complex[T]): Complex[T]">`*`[T](x: T; y: Complex[T]): Complex[T]</a></li>
    81. 

  81. 

  82. </ul>
    83. 

  83. <ul class="simple nested-toc-section">*=
    84. 

  84.   <li><a class="reference" href="#%2A%3D%2CComplex%5BT%5D%2CComplex%5BT%5D" title="`*=`[T](x: var Complex[T]; y: Complex[T])">`*=`[T](x: var Complex[T]; y: Complex[T])</a></li>
    85. 

  85. 

  86. </ul>
    87. 

  87. <ul class="simple nested-toc-section">+
    88. 

  88.   <li><a class="reference" href="#%2B%2CComplex%5BT%5D%2CComplex%5BT%5D" title="`+`[T](x, y: Complex[T]): Complex[T]">`+`[T](x, y: Complex[T]): Complex[T]</a></li>
    89. 

  89. <li><a class="reference" href="#%2B%2CComplex%5BT%5D%2CT" title="`+`[T](x: Complex[T]; y: T): Complex[T]">`+`[T](x: Complex[T]; y: T): Complex[T]</a></li>
    90. 

  90. <li><a class="reference" href="#%2B%2CT%2CComplex%5BT%5D" title="`+`[T](x: T; y: Complex[T]): Complex[T]">`+`[T](x: T; y: Complex[T]): Complex[T]</a></li>
    91. 

  91. 

  92. </ul>
    93. 

  93. <ul class="simple nested-toc-section">+=
    94. 

  94.   <li><a class="reference" href="#%2B%3D%2CComplex%5BT%5D%2CComplex%5BT%5D" title="`+=`[T](x: var Complex[T]; y: Complex[T])">`+=`[T](x: var Complex[T]; y: Complex[T])</a></li>
    95. 

  95. 

  96. </ul>
    97. 

  97. <ul class="simple nested-toc-section">-
    98. 

  98.   <li><a class="reference" href="#-%2CComplex%5BT%5D%2CComplex%5BT%5D" title="`-`[T](x, y: Complex[T]): Complex[T]">`-`[T](x, y: Complex[T]): Complex[T]</a></li>
    99. 

  99. <li><a class="reference" href="#-%2CComplex%5BT%5D%2CT" title="`-`[T](x: Complex[T]; y: T): Complex[T]">`-`[T](x: Complex[T]; y: T): Complex[T]</a></li>
    100. 

  100. <li><a class="reference" href="#-%2CT%2CComplex%5BT%5D" title="`-`[T](x: T; y: Complex[T]): Complex[T]">`-`[T](x: T; y: Complex[T]): Complex[T]</a></li>
    101. 

  101. <li><a class="reference" href="#-%2CComplex%5BT%5D" title="`-`[T](z: Complex[T]): Complex[T]">`-`[T](z: Complex[T]): Complex[T]</a></li>
    102. 

  102. 

  103. </ul>
    104. 

  104. <ul class="simple nested-toc-section">-=
    105. 

  105.   <li><a class="reference" href="#-%3D%2CComplex%5BT%5D%2CComplex%5BT%5D" title="`-=`[T](x: var Complex[T]; y: Complex[T])">`-=`[T](x: var Complex[T]; y: Complex[T])</a></li>
    106. 

  106. 

  107. </ul>
    108. 

  108. <ul class="simple nested-toc-section">/
    109. 

  109.   <li><a class="reference" href="#%2F%2CComplex%5BT%5D%2CComplex%5BT%5D" title="`/`[T](x, y: Complex[T]): Complex[T]">`/`[T](x, y: Complex[T]): Complex[T]</a></li>
    110. 

  110. <li><a class="reference" href="#%2F%2CComplex%5BT%5D%2CT" title="`/`[T](x: Complex[T]; y: T): Complex[T]">`/`[T](x: Complex[T]; y: T): Complex[T]</a></li>
    111. 

  111. <li><a class="reference" href="#%2F%2CT%2CComplex%5BT%5D" title="`/`[T](x: T; y: Complex[T]): Complex[T]">`/`[T](x: T; y: Complex[T]): Complex[T]</a></li>
    112. 

  112. 

  113. </ul>
    114. 

  114. <ul class="simple nested-toc-section">/=
    115. 

  115.   <li><a class="reference" href="#%2F%3D%2CComplex%5BT%5D%2CComplex%5BT%5D" title="`/=`[T](x: var Complex[T]; y: Complex[T])">`/=`[T](x: var Complex[T]; y: Complex[T])</a></li>
    116. 

  116. 

  117. </ul>
    118. 

  118. <ul class="simple nested-toc-section">==
    119. 

  119.   <li><a class="reference" href="#%3D%3D%2CComplex%5BT%5D%2CComplex%5BT%5D" title="`==`[T](x, y: Complex[T]): bool">`==`[T](x, y: Complex[T]): bool</a></li>
    120. 

  120. 

  121. </ul>
    122. 

  122. <ul class="simple nested-toc-section">abs
    123. 

  123.   <li><a class="reference" href="#abs%2CComplex%5BT%5D" title="abs[T](z: Complex[T]): T">abs[T](z: Complex[T]): T</a></li>
    124. 

  124. 

  125. </ul>
    126. 

  126. <ul class="simple nested-toc-section">abs2
    127. 

  127.   <li><a class="reference" href="#abs2%2CComplex%5BT%5D" title="abs2[T](z: Complex[T]): T">abs2[T](z: Complex[T]): T</a></li>
    128. 

  128. 

  129. </ul>
    130. 

  130. <ul class="simple nested-toc-section">almostEqual
    131. 

  131.   <li><a class="reference" href="#almostEqual%2CComplex%5BT%3A%20SomeFloat%5D%2CComplex%5BT%3A%20SomeFloat%5D%2CNatural" title="almostEqual[T: SomeFloat](x, y: Complex[T]; unitsInLastPlace: Natural = 4): bool">almostEqual[T: SomeFloat](x, y: Complex[T]; unitsInLastPlace: Natural = 4): bool</a></li>
    132. 

  132. 

  133. </ul>
    134. 

  134. <ul class="simple nested-toc-section">arccos
    135. 

  135.   <li><a class="reference" href="#arccos%2CComplex%5BT%5D" title="arccos[T](z: Complex[T]): Complex[T]">arccos[T](z: Complex[T]): Complex[T]</a></li>
    136. 

  136. 

  137. </ul>
    138. 

  138. <ul class="simple nested-toc-section">arccosh
    139. 

  139.   <li><a class="reference" href="#arccosh%2CComplex%5BT%5D" title="arccosh[T](z: Complex[T]): Complex[T]">arccosh[T](z: Complex[T]): Complex[T]</a></li>
    140. 

  140. 

  141. </ul>
    142. 

  142. <ul class="simple nested-toc-section">arccot
    143. 

  143.   <li><a class="reference" href="#arccot%2CComplex%5BT%5D" title="arccot[T](z: Complex[T]): Complex[T]">arccot[T](z: Complex[T]): Complex[T]</a></li>
    144. 

  144. 

  145. </ul>
    146. 

  146. <ul class="simple nested-toc-section">arccoth
    147. 

  147.   <li><a class="reference" href="#arccoth%2CComplex%5BT%5D" title="arccoth[T](z: Complex[T]): Complex[T]">arccoth[T](z: Complex[T]): Complex[T]</a></li>
    148. 

  148. 

  149. </ul>
    150. 

  150. <ul class="simple nested-toc-section">arccsc
    151. 

  151.   <li><a class="reference" href="#arccsc%2CComplex%5BT%5D" title="arccsc[T](z: Complex[T]): Complex[T]">arccsc[T](z: Complex[T]): Complex[T]</a></li>
    152. 

  152. 

  153. </ul>
    154. 

  154. <ul class="simple nested-toc-section">arccsch
    155. 

  155.   <li><a class="reference" href="#arccsch%2CComplex%5BT%5D" title="arccsch[T](z: Complex[T]): Complex[T]">arccsch[T](z: Complex[T]): Complex[T]</a></li>
    156. 

  156. 

  157. </ul>
    158. 

  158. <ul class="simple nested-toc-section">arcsec
    159. 

  159.   <li><a class="reference" href="#arcsec%2CComplex%5BT%5D" title="arcsec[T](z: Complex[T]): Complex[T]">arcsec[T](z: Complex[T]): Complex[T]</a></li>
    160. 

  160. 

  161. </ul>
    162. 

  162. <ul class="simple nested-toc-section">arcsech
    163. 

  163.   <li><a class="reference" href="#arcsech%2CComplex%5BT%5D" title="arcsech[T](z: Complex[T]): Complex[T]">arcsech[T](z: Complex[T]): Complex[T]</a></li>
    164. 

  164. 

  165. </ul>
    166. 

  166. <ul class="simple nested-toc-section">arcsin
    167. 

  167.   <li><a class="reference" href="#arcsin%2CComplex%5BT%5D" title="arcsin[T](z: Complex[T]): Complex[T]">arcsin[T](z: Complex[T]): Complex[T]</a></li>
    168. 

  168. 

  169. </ul>
    170. 

  170. <ul class="simple nested-toc-section">arcsinh
    171. 

  171.   <li><a class="reference" href="#arcsinh%2CComplex%5BT%5D" title="arcsinh[T](z: Complex[T]): Complex[T]">arcsinh[T](z: Complex[T]): Complex[T]</a></li>
    172. 

  172. 

  173. </ul>
    174. 

  174. <ul class="simple nested-toc-section">arctan
    175. 

  175.   <li><a class="reference" href="#arctan%2CComplex%5BT%5D" title="arctan[T](z: Complex[T]): Complex[T]">arctan[T](z: Complex[T]): Complex[T]</a></li>
    176. 

  176. 

  177. </ul>
    178. 

  178. <ul class="simple nested-toc-section">arctanh
    179. 

  179.   <li><a class="reference" href="#arctanh%2CComplex%5BT%5D" title="arctanh[T](z: Complex[T]): Complex[T]">arctanh[T](z: Complex[T]): Complex[T]</a></li>
    180. 

  180. 

  181. </ul>
    182. 

  182. <ul class="simple nested-toc-section">complex
    183. 

  183.   <li><a class="reference" href="#complex%2CT%2CT" title="complex[T: SomeFloat](re: T; im: T = 0.0): Complex[T]">complex[T: SomeFloat](re: T; im: T = 0.0): Complex[T]</a></li>
    184. 

  184. 

  185. </ul>
    186. 

  186. <ul class="simple nested-toc-section">complex32
    187. 

  187.   <li><a class="reference" href="#complex32%2Cfloat32%2Cfloat32" title="complex32(re: float32; im: float32 = 0.0): Complex32">complex32(re: float32; im: float32 = 0.0): Complex32</a></li>
    188. 

  188. 

  189. </ul>
    190. 

  190. <ul class="simple nested-toc-section">complex64
    191. 

  191.   <li><a class="reference" href="#complex64%2Cfloat64%2Cfloat64" title="complex64(re: float64; im: float64 = 0.0): Complex64">complex64(re: float64; im: float64 = 0.0): Complex64</a></li>
    192. 

  192. 

  193. </ul>
    194. 

  194. <ul class="simple nested-toc-section">conjugate
    195. 

  195.   <li><a class="reference" href="#conjugate%2CComplex%5BT%5D" title="conjugate[T](z: Complex[T]): Complex[T]">conjugate[T](z: Complex[T]): Complex[T]</a></li>
    196. 

  196. 

  197. </ul>
    198. 

  198. <ul class="simple nested-toc-section">cos
    199. 

  199.   <li><a class="reference" href="#cos%2CComplex%5BT%5D" title="cos[T](z: Complex[T]): Complex[T]">cos[T](z: Complex[T]): Complex[T]</a></li>
    200. 

  200. 

  201. </ul>
    202. 

  202. <ul class="simple nested-toc-section">cosh
    203. 

  203.   <li><a class="reference" href="#cosh%2CComplex%5BT%5D" title="cosh[T](z: Complex[T]): Complex[T]">cosh[T](z: Complex[T]): Complex[T]</a></li>
    204. 

  204. 

  205. </ul>
    206. 

  206. <ul class="simple nested-toc-section">cot
    207. 

  207.   <li><a class="reference" href="#cot%2CComplex%5BT%5D" title="cot[T](z: Complex[T]): Complex[T]">cot[T](z: Complex[T]): Complex[T]</a></li>
    208. 

  208. 

  209. </ul>
    210. 

  210. <ul class="simple nested-toc-section">coth
    211. 

  211.   <li><a class="reference" href="#coth%2CComplex%5BT%5D" title="coth[T](z: Complex[T]): Complex[T]">coth[T](z: Complex[T]): Complex[T]</a></li>
    212. 

  212. 

  213. </ul>
    214. 

  214. <ul class="simple nested-toc-section">csc
    215. 

  215.   <li><a class="reference" href="#csc%2CComplex%5BT%5D" title="csc[T](z: Complex[T]): Complex[T]">csc[T](z: Complex[T]): Complex[T]</a></li>
    216. 

  216. 

  217. </ul>
    218. 

  218. <ul class="simple nested-toc-section">csch
    219. 

  219.   <li><a class="reference" href="#csch%2CComplex%5BT%5D" title="csch[T](z: Complex[T]): Complex[T]">csch[T](z: Complex[T]): Complex[T]</a></li>
    220. 

  220. 

  221. </ul>
    222. 

  222. <ul class="simple nested-toc-section">exp
    223. 

  223.   <li><a class="reference" href="#exp%2CComplex%5BT%5D" title="exp[T](z: Complex[T]): Complex[T]">exp[T](z: Complex[T]): Complex[T]</a></li>
    224. 

  224. 

  225. </ul>
    226. 

  226. <ul class="simple nested-toc-section">formatValue
    227. 

  227.   <li><a class="reference" href="#formatValue%2Cstring%2CComplex%2Cstring" title="formatValue(result: var string; value: Complex; specifier: string)">formatValue(result: var string; value: Complex; specifier: string)</a></li>
    228. 

  228. 

  229. </ul>
    230. 

  230. <ul class="simple nested-toc-section">inv
    231. 

  231.   <li><a class="reference" href="#inv%2CComplex%5BT%5D" title="inv[T](z: Complex[T]): Complex[T]">inv[T](z: Complex[T]): Complex[T]</a></li>
    232. 

  232. 

  233. </ul>
    234. 

  234. <ul class="simple nested-toc-section">ln
    235. 

  235.   <li><a class="reference" href="#ln%2CComplex%5BT%5D" title="ln[T](z: Complex[T]): Complex[T]">ln[T](z: Complex[T]): Complex[T]</a></li>
    236. 

  236. 

  237. </ul>
    238. 

  238. <ul class="simple nested-toc-section">log2
    239. 

  239.   <li><a class="reference" href="#log2%2CComplex%5BT%5D" title="log2[T](z: Complex[T]): Complex[T]">log2[T](z: Complex[T]): Complex[T]</a></li>
    240. 

  240. 

  241. </ul>
    242. 

  242. <ul class="simple nested-toc-section">log10
    243. 

  243.   <li><a class="reference" href="#log10%2CComplex%5BT%5D" title="log10[T](z: Complex[T]): Complex[T]">log10[T](z: Complex[T]): Complex[T]</a></li>
    244. 

  244. 

  245. </ul>
    246. 

  246. <ul class="simple nested-toc-section">phase
    247. 

  247.   <li><a class="reference" href="#phase%2CComplex%5BT%5D" title="phase[T](z: Complex[T]): T">phase[T](z: Complex[T]): T</a></li>
    248. 

  248. 

  249. </ul>
    250. 

  250. <ul class="simple nested-toc-section">polar
    251. 

  251.   <li><a class="reference" href="#polar%2CComplex%5BT%5D" title="polar[T](z: Complex[T]): tuple[r, phi: T]">polar[T](z: Complex[T]): tuple[r, phi: T]</a></li>
    252. 

  252. 

  253. </ul>
    254. 

  254. <ul class="simple nested-toc-section">pow
    255. 

  255.   <li><a class="reference" href="#pow%2CComplex%5BT%5D%2CComplex%5BT%5D" title="pow[T](x, y: Complex[T]): Complex[T]">pow[T](x, y: Complex[T]): Complex[T]</a></li>
    256. 

  256. <li><a class="reference" href="#pow%2CComplex%5BT%5D%2CT" title="pow[T](x: Complex[T]; y: T): Complex[T]">pow[T](x: Complex[T]; y: T): Complex[T]</a></li>
    257. 

  257. 

  258. </ul>
    259. 

  259. <ul class="simple nested-toc-section">rect
    260. 

  260.   <li><a class="reference" href="#rect%2CT%2CT" title="rect[T](r, phi: T): Complex[T]">rect[T](r, phi: T): Complex[T]</a></li>
    261. 

  261. 

  262. </ul>
    263. 

  263. <ul class="simple nested-toc-section">sec
    264. 

  264.   <li><a class="reference" href="#sec%2CComplex%5BT%5D" title="sec[T](z: Complex[T]): Complex[T]">sec[T](z: Complex[T]): Complex[T]</a></li>
    265. 

  265. 

  266. </ul>
    267. 

  267. <ul class="simple nested-toc-section">sech
    268. 

  268.   <li><a class="reference" href="#sech%2CComplex%5BT%5D" title="sech[T](z: Complex[T]): Complex[T]">sech[T](z: Complex[T]): Complex[T]</a></li>
    269. 

  269. 

  270. </ul>
    271. 

  271. <ul class="simple nested-toc-section">sgn
    272. 

  272.   <li><a class="reference" href="#sgn%2CComplex%5BT%5D" title="sgn[T](z: Complex[T]): Complex[T]">sgn[T](z: Complex[T]): Complex[T]</a></li>
    273. 

  273. 

  274. </ul>
    275. 

  275. <ul class="simple nested-toc-section">sin
    276. 

  276.   <li><a class="reference" href="#sin%2CComplex%5BT%5D" title="sin[T](z: Complex[T]): Complex[T]">sin[T](z: Complex[T]): Complex[T]</a></li>
    277. 

  277. 

  278. </ul>
    279. 

  279. <ul class="simple nested-toc-section">sinh
    280. 

  280.   <li><a class="reference" href="#sinh%2CComplex%5BT%5D" title="sinh[T](z: Complex[T]): Complex[T]">sinh[T](z: Complex[T]): Complex[T]</a></li>
    281. 

  281. 

  282. </ul>
    283. 

  283. <ul class="simple nested-toc-section">sqrt
    284. 

  284.   <li><a class="reference" href="#sqrt%2CComplex%5BT%5D" title="sqrt[T](z: Complex[T]): Complex[T]">sqrt[T](z: Complex[T]): Complex[T]</a></li>
    285. 

  285. 

  286. </ul>
    287. 

  287. <ul class="simple nested-toc-section">tan
    288. 

  288.   <li><a class="reference" href="#tan%2CComplex%5BT%5D" title="tan[T](z: Complex[T]): Complex[T]">tan[T](z: Complex[T]): Complex[T]</a></li>
    289. 

  289. 

  290. </ul>
    291. 

  291. <ul class="simple nested-toc-section">tanh
    292. 

  292.   <li><a class="reference" href="#tanh%2CComplex%5BT%5D" title="tanh[T](z: Complex[T]): Complex[T]">tanh[T](z: Complex[T]): Complex[T]</a></li>
    293. 

  293. 

  294. </ul>
    295. 

  295. 

  296.     </ul>
    297. 

  297.   </details>
    298. 

  298. </li>
    299. 

  299. <li>
    300. 

  300.   <details open>
    301. 

  301.     <summary><a class="reference reference-toplevel" href="#18" id="68">Templates</a></summary>
    302. 

  302.     <ul class="simple simple-toc-section">
    303. 

  303.       <ul class="simple nested-toc-section">im
    304. 

  304.   <li><a class="reference" href="#im.t%2Cfloat32" title="im(arg: float32): Complex32">im(arg: float32): Complex32</a></li>
    305. 

  305. <li><a class="reference" href="#im.t%2Cfloat64" title="im(arg: float64): Complex64">im(arg: float64): Complex64</a></li>
    306. 

  306. <li><a class="reference" href="#im.t%2Ctypedesc%5Bfloat32%5D" title="im(arg: typedesc[float32]): Complex32">im(arg: typedesc[float32]): Complex32</a></li>
    307. 

  307. <li><a class="reference" href="#im.t%2Ctypedesc%5Bfloat64%5D" title="im(arg: typedesc[float64]): Complex64">im(arg: typedesc[float64]): Complex64</a></li>
    308. 

  308. 

  309. </ul>
    310. 

  310. 

  311.     </ul>
    312. 

  312.   </details>
    313. 

  313. </li>
    314. 

  314. 

  315. </ul>
    316. 

  316. 

  317.   </div>
    318. 

  318.   <div class="nine columns" id="content">
    319. 

  319.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L1" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    320. 

  320. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L1" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    321. 

  321. 

  322.     <div id="tocRoot"></div>
    323. 

  323.     
    324. 

  324.     <p class="module-desc"><p>This module implements complex numbers and basic mathematical operations on them.</p>
    325. 

  325. <p>Complex numbers are currently generic over 64-bit or 32-bit floats.</p>
    326. 

  326. 

  327. <p><strong class="examples_text">Example:</strong></p>
    328. 

  328. <pre class="listing"><span class="Keyword">import</span> <span class="Identifier">std</span><span class="Operator">/</span><span class="Identifier">complex</span>
    329. 

  329. <span class="Keyword">from</span> <span class="Identifier">std</span><span class="Operator">/</span><span class="Identifier">math</span> <span class="Keyword">import</span> <span class="Identifier">almostEqual</span><span class="Punctuation">,</span> <span class="Identifier">sqrt</span>
    330. 

  330. 

  331. <span class="Keyword">let</span>
    332. 

  332.   <span class="Identifier">z1</span> <span class="Operator">=</span> <span class="Identifier">complex</span><span class="Punctuation">(</span><span class="FloatNumber">1.0</span><span class="Punctuation">,</span> <span class="FloatNumber">2.0</span><span class="Punctuation">)</span>
    333. 

  333.   <span class="Identifier">z2</span> <span class="Operator">=</span> <span class="Identifier">complex</span><span class="Punctuation">(</span><span class="FloatNumber">3.0</span><span class="Punctuation">,</span> <span class="Operator">-</span><span class="FloatNumber">4.0</span><span class="Punctuation">)</span>
    334. 

  334. 

  335. <span class="Identifier">assert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">z1</span> <span class="Operator">+</span> <span class="Identifier">z2</span><span class="Punctuation">,</span> <span class="Identifier">complex</span><span class="Punctuation">(</span><span class="FloatNumber">4.0</span><span class="Punctuation">,</span> <span class="Operator">-</span><span class="FloatNumber">2.0</span><span class="Punctuation">)</span><span class="Punctuation">)</span>
    336. 

  336. <span class="Identifier">assert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">z1</span> <span class="Operator">-</span> <span class="Identifier">z2</span><span class="Punctuation">,</span> <span class="Identifier">complex</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="FloatNumber">2.0</span><span class="Punctuation">,</span> <span class="FloatNumber">6.0</span><span class="Punctuation">)</span><span class="Punctuation">)</span>
    337. 

  337. <span class="Identifier">assert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">z1</span> <span class="Operator">*</span> <span class="Identifier">z2</span><span class="Punctuation">,</span> <span class="Identifier">complex</span><span class="Punctuation">(</span><span class="FloatNumber">11.0</span><span class="Punctuation">,</span> <span class="FloatNumber">2.0</span><span class="Punctuation">)</span><span class="Punctuation">)</span>
    338. 

  338. <span class="Identifier">assert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">z1</span> <span class="Operator">/</span> <span class="Identifier">z2</span><span class="Punctuation">,</span> <span class="Identifier">complex</span><span class="Punctuation">(</span><span class="Operator">-</span><span class="FloatNumber">0.2</span><span class="Punctuation">,</span> <span class="FloatNumber">0.4</span><span class="Punctuation">)</span><span class="Punctuation">)</span>
    339. 

  339. 

  340. <span class="Identifier">assert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">abs</span><span class="Punctuation">(</span><span class="Identifier">z1</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="Identifier">sqrt</span><span class="Punctuation">(</span><span class="FloatNumber">5.0</span><span class="Punctuation">)</span><span class="Punctuation">)</span>
    341. 

  341. <span class="Identifier">assert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">conjugate</span><span class="Punctuation">(</span><span class="Identifier">z1</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="Identifier">complex</span><span class="Punctuation">(</span><span class="FloatNumber">1.0</span><span class="Punctuation">,</span> <span class="Operator">-</span><span class="FloatNumber">2.0</span><span class="Punctuation">)</span><span class="Punctuation">)</span>
    342. 

  342. 

  343. <span class="Keyword">let</span> <span class="Punctuation">(</span><span class="Identifier">r</span><span class="Punctuation">,</span> <span class="Identifier">phi</span><span class="Punctuation">)</span> <span class="Operator">=</span> <span class="Identifier">z1</span><span class="Operator">.</span><span class="Identifier">polar</span>
    344. 

  344. <span class="Identifier">assert</span> <span class="Identifier">almostEqual</span><span class="Punctuation">(</span><span class="Identifier">rect</span><span class="Punctuation">(</span><span class="Identifier">r</span><span class="Punctuation">,</span> <span class="Identifier">phi</span><span class="Punctuation">)</span><span class="Punctuation">,</span> <span class="Identifier">z1</span><span class="Punctuation">)</span></pre></p>
    345. 

  345.     <div class="section" id="6">
    346. 

  346.   <h1><a class="toc-backref" href="#6">Imports</a></h1>
    347. 

  347.   <dl class="item">
    348. 

  348.     <a class="reference external" href="math.html">math</a>, <a class="reference external" href="strformat.html">strformat</a>, <a class="reference external" href="strutils.html">strutils</a>
    349. 

  349.   </dl>
    350. 

  350. </div>
    351. 

  351. <div class="section" id="7">
    352. 

  352.   <h1><a class="toc-backref" href="#7">Types</a></h1>
    353. 

  353.   <dl class="item">
    354. 

  354.     <div id="Complex">
    355. 

  355.   <dt><pre><a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span> <span class="Other">=</span> <span class="Keyword">object</span>
    356. 

  356.   <span class="Identifier">re</span><span class="Operator">*</span><span class="Other">,</span> <span class="Identifier">im</span><span class="Operator">*</span><span class="Other">:</span> <span class="Identifier">T</span></pre></dt>
    357. 

  357.   <dd>
    358. 

  358.     
    359. 

  359.     A complex number, consisting of a real and an imaginary part.
    360. 

  360.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L39" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    361. 

  361. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L39" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    362. 

  362. 

  363.   </dd>
    364. 

  364. </div>
    365. 

  365. <div id="Complex32">
    366. 

  366.   <dt><pre><a href="complex.html#Complex32"><span class="Identifier">Complex32</span></a> <span class="Other">=</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">]</span></pre></dt>
    367. 

  367.   <dd>
    368. 

  368.     
    369. 

  369.     Alias for a complex number using 32-bit floats.
    370. 

  370.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L44" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    371. 

  371. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L44" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    372. 

  372. 

  373.   </dd>
    374. 

  374. </div>
    375. 

  375. <div id="Complex64">
    376. 

  376.   <dt><pre><a href="complex.html#Complex64"><span class="Identifier">Complex64</span></a> <span class="Other">=</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">]</span></pre></dt>
    377. 

  377.   <dd>
    378. 

  378.     
    379. 

  379.     Alias for a complex number using 64-bit floats.
    380. 

  380.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L42" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    381. 

  381. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L42" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    382. 

  382. 

  383.   </dd>
    384. 

  384. </div>
    385. 

  385. 

  386.   </dl>
    387. 

  387. </div>
    388. 

  388. <div class="section" id="12">
    389. 

  389.   <h1><a class="toc-backref" href="#12">Procs</a></h1>
    390. 

  390.   <dl class="item">
    391. 

  391.     <div id="$-procs-all">
    392. 

  392.   <div id="$,Complex">
    393. 

  393.   <dt><pre><span class="Keyword">func</span> <a href="#%24%2CComplex"><span class="Identifier">`$`</span></a><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">)</span><span class="Other">:</span> <a href="system.html#string"><span class="Identifier">string</span></a></pre></dt>
    394. 

  394.   <dd>
    395. 

  395.     
    396. 

  396.     Returns <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>'s string representation as <tt class="docutils literal"><span class="pre"><span class="StringLit">&quot;(re, im)&quot;</span></span></tt>.
    397. 

  397. <p><strong class="examples_text">Example:</strong></p>
    398. 

  398. <pre class="listing"><span class="Identifier">doAssert</span> <span class="Operator">$</span><span class="Identifier">complex</span><span class="Punctuation">(</span><span class="FloatNumber">1.0</span><span class="Punctuation">,</span> <span class="FloatNumber">2.0</span><span class="Punctuation">)</span> <span class="Operator">==</span> <span class="StringLit">&quot;(1.0, 2.0)&quot;</span></pre>
    399. 

  399.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L410" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    400. 

  400. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L410" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    401. 

  401. 

  402.   </dd>
    403. 

  403. </div>
    404. 

  404. 

  405. </div>
    406. 

  406. <div id="*-procs-all">
    407. 

  407.   <div id="*,Complex[T],Complex[T]">
    408. 

  408.   <dt><pre><span class="Keyword">func</span> <a href="#%2A%2CComplex%5BT%5D%2CComplex%5BT%5D"><span class="Identifier">`*`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    409. 

  409.   <dd>
    410. 

  410.     
    411. 

  411.     Multiplies two complex numbers.
    412. 

  412.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L136" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    413. 

  413. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L136" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    414. 

  414. 

  415.   </dd>
    416. 

  416. </div>
    417. 

  417. <div id="*,Complex[T],T">
    418. 

  418.   <dt><pre><span class="Keyword">func</span> <a href="#%2A%2CComplex%5BT%5D%2CT"><span class="Identifier">`*`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    419. 

  419.   <dd>
    420. 

  420.     
    421. 

  421.     Multiplies a complex number with a real number.
    422. 

  422.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L132" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    423. 

  423. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L132" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    424. 

  424. 

  425.   </dd>
    426. 

  426. </div>
    427. 

  427. <div id="*,T,Complex[T]">
    428. 

  428.   <dt><pre><span class="Keyword">func</span> <a href="#%2A%2CT%2CComplex%5BT%5D"><span class="Identifier">`*`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    429. 

  429.   <dd>
    430. 

  430.     
    431. 

  431.     Multiplies a real number with a complex number.
    432. 

  432.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L128" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    433. 

  433. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L128" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    434. 

  434. 

  435.   </dd>
    436. 

  436. </div>
    437. 

  437. 

  438. </div>
    439. 

  439. <div id="*=-procs-all">
    440. 

  440.   <div id="*=,Complex[T],Complex[T]">
    441. 

  441.   <dt><pre><span class="Keyword">func</span> <a href="#%2A%3D%2CComplex%5BT%5D%2CComplex%5BT%5D"><span class="Identifier">`*=`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span></pre></dt>
    442. 

  442.   <dd>
    443. 

  443.     
    444. 

  444.     Multiplies <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> by <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.
    445. 

  445.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L163" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    446. 

  446. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L163" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    447. 

  447. 

  448.   </dd>
    449. 

  449. </div>
    450. 

  450. 

  451. </div>
    452. 

  452. <div id="+-procs-all">
    453. 

  453.   <div id="+,Complex[T],Complex[T]">
    454. 

  454.   <dt><pre><span class="Keyword">func</span> <a href="#%2B%2CComplex%5BT%5D%2CComplex%5BT%5D"><span class="Identifier">`+`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    455. 

  455.   <dd>
    456. 

  456.     
    457. 

  457.     Adds two complex numbers.
    458. 

  458.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L108" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    459. 

  459. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L108" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    460. 

  460. 

  461.   </dd>
    462. 

  462. </div>
    463. 

  463. <div id="+,Complex[T],T">
    464. 

  464.   <dt><pre><span class="Keyword">func</span> <a href="#%2B%2CComplex%5BT%5D%2CT"><span class="Identifier">`+`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    465. 

  465.   <dd>
    466. 

  466.     
    467. 

  467.     Adds a complex number to a real number.
    468. 

  468.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L104" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    469. 

  469. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L104" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    470. 

  470. 

  471.   </dd>
    472. 

  472. </div>
    473. 

  473. <div id="+,T,Complex[T]">
    474. 

  474.   <dt><pre><span class="Keyword">func</span> <a href="#%2B%2CT%2CComplex%5BT%5D"><span class="Identifier">`+`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    475. 

  475.   <dd>
    476. 

  476.     
    477. 

  477.     Adds a real number to a complex number.
    478. 

  478.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L100" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    479. 

  479. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L100" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    480. 

  480. 

  481.   </dd>
    482. 

  482. </div>
    483. 

  483. 

  484. </div>
    485. 

  485. <div id="+=-procs-all">
    486. 

  486.   <div id="+=,Complex[T],Complex[T]">
    487. 

  487.   <dt><pre><span class="Keyword">func</span> <a href="#%2B%3D%2CComplex%5BT%5D%2CComplex%5BT%5D"><span class="Identifier">`+=`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span></pre></dt>
    488. 

  488.   <dd>
    489. 

  489.     
    490. 

  490.     Adds <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> to <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.
    491. 

  491.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L153" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    492. 

  492. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L153" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    493. 

  493. 

  494.   </dd>
    495. 

  495. </div>
    496. 

  496. 

  497. </div>
    498. 

  498. <div id="--procs-all">
    499. 

  499.   <div id="-,Complex[T],Complex[T]">
    500. 

  500.   <dt><pre><span class="Keyword">func</span> <a href="#-%2CComplex%5BT%5D%2CComplex%5BT%5D"><span class="Identifier">`-`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    501. 

  501.   <dd>
    502. 

  502.     
    503. 

  503.     Subtracts two complex numbers.
    504. 

  504.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L124" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    505. 

  505. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L124" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    506. 

  506. 

  507.   </dd>
    508. 

  508. </div>
    509. 

  509. <div id="-,Complex[T],T">
    510. 

  510.   <dt><pre><span class="Keyword">func</span> <a href="#-%2CComplex%5BT%5D%2CT"><span class="Identifier">`-`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    511. 

  511.   <dd>
    512. 

  512.     
    513. 

  513.     Subtracts a real number from a complex number.
    514. 

  514.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L120" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    515. 

  515. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L120" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    516. 

  516. 

  517.   </dd>
    518. 

  518. </div>
    519. 

  519. <div id="-,T,Complex[T]">
    520. 

  520.   <dt><pre><span class="Keyword">func</span> <a href="#-%2CT%2CComplex%5BT%5D"><span class="Identifier">`-`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    521. 

  521.   <dd>
    522. 

  522.     
    523. 

  523.     Subtracts a complex number from a real number.
    524. 

  524.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L116" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    525. 

  525. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L116" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    526. 

  526. 

  527.   </dd>
    528. 

  528. </div>
    529. 

  529. <div id="-,Complex[T]">
    530. 

  530.   <dt><pre><span class="Keyword">func</span> <a href="#-%2CComplex%5BT%5D"><span class="Identifier">`-`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    531. 

  531.   <dd>
    532. 

  532.     
    533. 

  533.     Unary minus for complex numbers.
    534. 

  534.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L112" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    535. 

  535. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L112" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    536. 

  536. 

  537.   </dd>
    538. 

  538. </div>
    539. 

  539. 

  540. </div>
    541. 

  541. <div id="-=-procs-all">
    542. 

  542.   <div id="-=,Complex[T],Complex[T]">
    543. 

  543.   <dt><pre><span class="Keyword">func</span> <a href="#-%3D%2CComplex%5BT%5D%2CComplex%5BT%5D"><span class="Identifier">`-=`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span></pre></dt>
    544. 

  544.   <dd>
    545. 

  545.     
    546. 

  546.     Subtracts <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> from <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt>.
    547. 

  547.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L158" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    548. 

  548. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L158" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    549. 

  549. 

  550.   </dd>
    551. 

  551. </div>
    552. 

  552. 

  553. </div>
    554. 

  554. <div id="/-procs-all">
    555. 

  555.   <div id="/,Complex[T],Complex[T]">
    556. 

  556.   <dt><pre><span class="Keyword">func</span> <a href="#%2F%2CComplex%5BT%5D%2CComplex%5BT%5D"><span class="Identifier">`/`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    557. 

  557.   <dd>
    558. 

  558.     
    559. 

  559.     Divides two complex numbers.
    560. 

  560.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L149" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    561. 

  561. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L149" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    562. 

  562. 

  563.   </dd>
    564. 

  564. </div>
    565. 

  565. <div id="/,Complex[T],T">
    566. 

  566.   <dt><pre><span class="Keyword">func</span> <a href="#%2F%2CComplex%5BT%5D%2CT"><span class="Identifier">`/`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    567. 

  567.   <dd>
    568. 

  568.     
    569. 

  569.     Divides a complex number by a real number.
    570. 

  570.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L141" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    571. 

  571. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L141" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    572. 

  572. 

  573.   </dd>
    574. 

  574. </div>
    575. 

  575. <div id="/,T,Complex[T]">
    576. 

  576.   <dt><pre><span class="Keyword">func</span> <a href="#%2F%2CT%2CComplex%5BT%5D"><span class="Identifier">`/`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    577. 

  577.   <dd>
    578. 

  578.     
    579. 

  579.     Divides a real number by a complex number.
    580. 

  580.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L145" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    581. 

  581. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L145" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    582. 

  582. 

  583.   </dd>
    584. 

  584. </div>
    585. 

  585. 

  586. </div>
    587. 

  587. <div id="/=-procs-all">
    588. 

  588.   <div id="/=,Complex[T],Complex[T]">
    589. 

  589.   <dt><pre><span class="Keyword">func</span> <a href="#%2F%3D%2CComplex%5BT%5D%2CComplex%5BT%5D"><span class="Identifier">`/=`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span></pre></dt>
    590. 

  590.   <dd>
    591. 

  591.     
    592. 

  592.     Divides <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> by <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt> in place.
    593. 

  593.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L169" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    594. 

  594. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L169" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    595. 

  595. 

  596.   </dd>
    597. 

  597. </div>
    598. 

  598. 

  599. </div>
    600. 

  600. <div id="==-procs-all">
    601. 

  601.   <div id="==,Complex[T],Complex[T]">
    602. 

  602.   <dt><pre><span class="Keyword">func</span> <a href="#%3D%3D%2CComplex%5BT%5D%2CComplex%5BT%5D"><span class="Identifier">`==`</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="system.html#bool"><span class="Identifier">bool</span></a></pre></dt>
    603. 

  603.   <dd>
    604. 

  604.     
    605. 

  605.     Compares two complex numbers for equality.
    606. 

  606.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L96" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    607. 

  607. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L96" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    608. 

  608. 

  609.   </dd>
    610. 

  610. </div>
    611. 

  611. 

  612. </div>
    613. 

  613. <div id="abs-procs-all">
    614. 

  614.   <div id="abs,Complex[T]">
    615. 

  615.   <dt><pre><span class="Keyword">func</span> <a href="#abs%2CComplex%5BT%5D"><span class="Identifier">abs</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">T</span></pre></dt>
    616. 

  616.   <dd>
    617. 

  617.     
    618. 

  618.     Returns the absolute value of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>, that is the distance from (0, 0) to <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
    619. 

  619.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L68" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    620. 

  620. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L68" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    621. 

  621. 

  622.   </dd>
    623. 

  623. </div>
    624. 

  624. 

  625. </div>
    626. 

  626. <div id="abs2-procs-all">
    627. 

  627.   <div id="abs2,Complex[T]">
    628. 

  628.   <dt><pre><span class="Keyword">func</span> <a href="#abs2%2CComplex%5BT%5D"><span class="Identifier">abs2</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">T</span></pre></dt>
    629. 

  629.   <dd>
    630. 

  630.     
    631. 

  631.     Returns the squared absolute value of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>, that is the squared distance from (0, 0) to <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>. This is more efficient than <tt class="docutils literal"><span class="pre"><span class="Identifier">abs</span><span class="Punctuation">(</span><span class="Identifier">z</span><span class="Punctuation">)</span> <span class="Operator">^</span> <span class="DecNumber">2</span></span></tt>.
    632. 

  632.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L73" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    633. 

  633. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L73" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    634. 

  634. 

  635.   </dd>
    636. 

  636. </div>
    637. 

  637. 

  638. </div>
    639. 

  639. <div id="almostEqual-procs-all">
    640. 

  640.   <div id="almostEqual,Complex[T: SomeFloat],Complex[T: SomeFloat],Natural">
    641. 

  641.   <dt><pre><span class="Keyword">func</span> <a href="#almostEqual%2CComplex%5BT%3A%20SomeFloat%5D%2CComplex%5BT%3A%20SomeFloat%5D%2CNatural"><span class="Identifier">almostEqual</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#SomeFloat"><span class="Identifier">SomeFloat</span></a><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">unitsInLastPlace</span><span class="Other">:</span> <a href="system.html#Natural"><span class="Identifier">Natural</span></a> <span class="Other">=</span> <span class="DecNumber">4</span><span class="Other">)</span><span class="Other">:</span> <a href="system.html#bool"><span class="Identifier">bool</span></a></pre></dt>
    642. 

  642.   <dd>
    643. 

  643.     
    644. 

  644.     <p>Checks if two complex values are almost equal, using the <a class="reference external" href="https://en.wikipedia.org/wiki/Machine_epsilon">machine epsilon</a>.</p>
    645. 

  645. <p>Two complex values are considered almost equal if their real and imaginary components are almost equal.</p>
    646. 

  646. <p><tt class="docutils literal"><span class="pre"><span class="Identifier">unitsInLastPlace</span></span></tt> is the max number of <a class="reference external" href="https://en.wikipedia.org/wiki/Unit_in_the_last_place">units in the last place</a> difference tolerated when comparing two numbers. The larger the value, the more error is allowed. A <tt class="docutils literal"><span class="pre"><span class="DecNumber">0</span></span></tt> value means that two numbers must be exactly the same to be considered equal.</p>
    647. 

  647. <p>The machine epsilon has to be scaled to the magnitude of the values used and multiplied by the desired precision in ULPs unless the difference is subnormal.</p>
    648. 

  648. 

  649.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L391" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    650. 

  650. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L391" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    651. 

  651. 

  652.   </dd>
    653. 

  653. </div>
    654. 

  654. 

  655. </div>
    656. 

  656. <div id="arccos-procs-all">
    657. 

  657.   <div id="arccos,Complex[T]">
    658. 

  658.   <dt><pre><span class="Keyword">func</span> <a href="#arccos%2CComplex%5BT%5D"><span class="Identifier">arccos</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    659. 

  659.   <dd>
    660. 

  660.     
    661. 

  661.     Returns the inverse cosine of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
    662. 

  662.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L281" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    663. 

  663. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L281" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    664. 

  664. 

  665.   </dd>
    666. 

  666. </div>
    667. 

  667. 

  668. </div>
    669. 

  669. <div id="arccosh-procs-all">
    670. 

  670.   <div id="arccosh,Complex[T]">
    671. 

  671.   <dt><pre><span class="Keyword">func</span> <a href="#arccosh%2CComplex%5BT%5D"><span class="Identifier">arccosh</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    672. 

  672.   <dd>
    673. 

  673.     
    674. 

  674.     Returns the inverse hyperbolic cosine of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
    675. 

  675.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L329" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    676. 

  676. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L329" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    677. 

  677. 

  678.   </dd>
    679. 

  679. </div>
    680. 

  680. 

  681. </div>
    682. 

  682. <div id="arccot-procs-all">
    683. 

  683.   <div id="arccot,Complex[T]">
    684. 

  684.   <dt><pre><span class="Keyword">func</span> <a href="#arccot%2CComplex%5BT%5D"><span class="Identifier">arccot</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    685. 

  685.   <dd>
    686. 

  686.     
    687. 

  687.     Returns the inverse cotangent of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
    688. 

  688.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L297" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    689. 

  689. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L297" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    690. 

  690. 

  691.   </dd>
    692. 

  692. </div>
    693. 

  693. 

  694. </div>
    695. 

  695. <div id="arccoth-procs-all">
    696. 

  696.   <div id="arccoth,Complex[T]">
    697. 

  697.   <dt><pre><span class="Keyword">func</span> <a href="#arccoth%2CComplex%5BT%5D"><span class="Identifier">arccoth</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    698. 

  698.   <dd>
    699. 

  699.     
    700. 

  700.     Returns the inverse hyperbolic cotangent of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
    701. 

  701.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L345" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    702. 

  702. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L345" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    703. 

  703. 

  704.   </dd>
    705. 

  705. </div>
    706. 

  706. 

  707. </div>
    708. 

  708. <div id="arccsc-procs-all">
    709. 

  709.   <div id="arccsc,Complex[T]">
    710. 

  710.   <dt><pre><span class="Keyword">func</span> <a href="#arccsc%2CComplex%5BT%5D"><span class="Identifier">arccsc</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    711. 

  711.   <dd>
    712. 

  712.     
    713. 

  713.     Returns the inverse cosecant of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
    714. 

  714.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L313" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    715. 

  715. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L313" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    716. 

  716. 

  717.   </dd>
    718. 

  718. </div>
    719. 

  719. 

  720. </div>
    721. 

  721. <div id="arccsch-procs-all">
    722. 

  722.   <div id="arccsch,Complex[T]">
    723. 

  723.   <dt><pre><span class="Keyword">func</span> <a href="#arccsch%2CComplex%5BT%5D"><span class="Identifier">arccsch</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    724. 

  724.   <dd>
    725. 

  725.     
    726. 

  726.     Returns the inverse hyperbolic cosecant of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
    727. 

  727.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L361" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    728. 

  728. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L361" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    729. 

  729. 

  730.   </dd>
    731. 

  731. </div>
    732. 

  732. 

  733. </div>
    734. 

  734. <div id="arcsec-procs-all">
    735. 

  735.   <div id="arcsec,Complex[T]">
    736. 

  736.   <dt><pre><span class="Keyword">func</span> <a href="#arcsec%2CComplex%5BT%5D"><span class="Identifier">arcsec</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    737. 

  737.   <dd>
    738. 

  738.     
    739. 

  739.     Returns the inverse secant of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
    740. 

  740.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L305" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    741. 

  741. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L305" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    742. 

  742. 

  743.   </dd>
    744. 

  744. </div>
    745. 

  745. 

  746. </div>
    747. 

  747. <div id="arcsech-procs-all">
    748. 

  748.   <div id="arcsech,Complex[T]">
    749. 

  749.   <dt><pre><span class="Keyword">func</span> <a href="#arcsech%2CComplex%5BT%5D"><span class="Identifier">arcsech</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    750. 

  750.   <dd>
    751. 

  751.     
    752. 

  752.     Returns the inverse hyperbolic secant of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
    753. 

  753.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L353" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    754. 

  754. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L353" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    755. 

  755. 

  756.   </dd>
    757. 

  757. </div>
    758. 

  758. 

  759. </div>
    760. 

  760. <div id="arcsin-procs-all">
    761. 

  761.   <div id="arcsin,Complex[T]">
    762. 

  762.   <dt><pre><span class="Keyword">func</span> <a href="#arcsin%2CComplex%5BT%5D"><span class="Identifier">arcsin</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    763. 

  763.   <dd>
    764. 

  764.     
    765. 

  765.     Returns the inverse sine of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
    766. 

  766.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L271" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    767. 

  767. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L271" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    768. 

  768. 

  769.   </dd>
    770. 

  770. </div>
    771. 

  771. 

  772. </div>
    773. 

  773. <div id="arcsinh-procs-all">
    774. 

  774.   <div id="arcsinh,Complex[T]">
    775. 

  775.   <dt><pre><span class="Keyword">func</span> <a href="#arcsinh%2CComplex%5BT%5D"><span class="Identifier">arcsinh</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    776. 

  776.   <dd>
    777. 

  777.     
    778. 

  778.     Returns the inverse hyperbolic sine of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
    779. 

  779.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L321" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    780. 

  780. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L321" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    781. 

  781. 

  782.   </dd>
    783. 

  783. </div>
    784. 

  784. 

  785. </div>
    786. 

  786. <div id="arctan-procs-all">
    787. 

  787.   <div id="arctan,Complex[T]">
    788. 

  788.   <dt><pre><span class="Keyword">func</span> <a href="#arctan%2CComplex%5BT%5D"><span class="Identifier">arctan</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    789. 

  789.   <dd>
    790. 

  790.     
    791. 

  791.     Returns the inverse tangent of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
    792. 

  792.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L289" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    793. 

  793. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L289" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    794. 

  794. 

  795.   </dd>
    796. 

  796. </div>
    797. 

  797. 

  798. </div>
    799. 

  799. <div id="arctanh-procs-all">
    800. 

  800.   <div id="arctanh,Complex[T]">
    801. 

  801.   <dt><pre><span class="Keyword">func</span> <a href="#arctanh%2CComplex%5BT%5D"><span class="Identifier">arctanh</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    802. 

  802.   <dd>
    803. 

  803.     
    804. 

  804.     Returns the inverse hyperbolic tangent of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
    805. 

  805.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L337" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    806. 

  806. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L337" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    807. 

  807. 

  808.   </dd>
    809. 

  809. </div>
    810. 

  810. 

  811. </div>
    812. 

  812. <div id="complex-procs-all">
    813. 

  813.   <div id="complex,T,T">
    814. 

  814.   <dt><pre><span class="Keyword">func</span> <a href="#complex%2CT%2CT"><span class="Identifier">complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">:</span> <a href="system.html#SomeFloat"><span class="Identifier">SomeFloat</span></a><span class="Other">]</span><span class="Other">(</span><span class="Identifier">re</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">;</span> <span class="Identifier">im</span><span class="Other">:</span> <span class="Identifier">T</span> <span class="Other">=</span> <span class="FloatNumber">0.0</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    815. 

  815.   <dd>
    816. 

  816.     
    817. 

  817.     Returns a <tt class="docutils literal"><span class="pre"><span class="Identifier">Complex</span><span class="Punctuation">[</span><span class="Identifier">T</span><span class="Punctuation">]</span></span></tt> with real part <tt class="docutils literal"><span class="pre"><span class="Identifier">re</span></span></tt> and imaginary part <tt class="docutils literal"><span class="pre"><span class="Identifier">im</span></span></tt>.
    818. 

  818.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L47" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    819. 

  819. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L47" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    820. 

  820. 

  821.   </dd>
    822. 

  822. </div>
    823. 

  823. 

  824. </div>
    825. 

  825. <div id="complex32-procs-all">
    826. 

  826.   <div id="complex32,float32,float32">
    827. 

  827.   <dt><pre><span class="Keyword">func</span> <a href="#complex32%2Cfloat32%2Cfloat32"><span class="Identifier">complex32</span></a><span class="Other">(</span><span class="Identifier">re</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">;</span> <span class="Identifier">im</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a> <span class="Other">=</span> <span class="FloatNumber">0.0</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex32"><span class="Identifier">Complex32</span></a> {.<span><span class="Other pragmadots">...</span></span><span class="pragmawrap"><span class="Identifier">raises</span><span class="Other">:</span> <span class="Other">[</span><span class="Other">]</span><span class="Other">,</span>
    828. 

  828.     <span class="Identifier">tags</span><span class="Other">:</span> <span class="Other">[</span><span class="Other">]</span><span class="Other">,</span> <span class="Identifier">forbids</span><span class="Other">:</span> <span class="Other">[</span><span class="Other">]</span></span>.}</pre></dt>
    829. 

  829.   <dd>
    830. 

  830.     
    831. 

  831.     Returns a <tt class="docutils literal"><span class="pre"><span class="Identifier">Complex32</span></span></tt> with real part <tt class="docutils literal"><span class="pre"><span class="Identifier">re</span></span></tt> and imaginary part <tt class="docutils literal"><span class="pre"><span class="Identifier">im</span></span></tt>.
    832. 

  832.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L51" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    833. 

  833. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L51" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    834. 

  834. 

  835.   </dd>
    836. 

  836. </div>
    837. 

  837. 

  838. </div>
    839. 

  839. <div id="complex64-procs-all">
    840. 

  840.   <div id="complex64,float64,float64">
    841. 

  841.   <dt><pre><span class="Keyword">func</span> <a href="#complex64%2Cfloat64%2Cfloat64"><span class="Identifier">complex64</span></a><span class="Other">(</span><span class="Identifier">re</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">;</span> <span class="Identifier">im</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a> <span class="Other">=</span> <span class="FloatNumber">0.0</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex64"><span class="Identifier">Complex64</span></a> {.<span><span class="Other pragmadots">...</span></span><span class="pragmawrap"><span class="Identifier">raises</span><span class="Other">:</span> <span class="Other">[</span><span class="Other">]</span><span class="Other">,</span>
    842. 

  842.     <span class="Identifier">tags</span><span class="Other">:</span> <span class="Other">[</span><span class="Other">]</span><span class="Other">,</span> <span class="Identifier">forbids</span><span class="Other">:</span> <span class="Other">[</span><span class="Other">]</span></span>.}</pre></dt>
    843. 

  843.   <dd>
    844. 

  844.     
    845. 

  845.     Returns a <tt class="docutils literal"><span class="pre"><span class="Identifier">Complex64</span></span></tt> with real part <tt class="docutils literal"><span class="pre"><span class="Identifier">re</span></span></tt> and imaginary part <tt class="docutils literal"><span class="pre"><span class="Identifier">im</span></span></tt>.
    846. 

  846.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L55" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    847. 

  847. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L55" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    848. 

  848. 

  849.   </dd>
    850. 

  850. </div>
    851. 

  851. 

  852. </div>
    853. 

  853. <div id="conjugate-procs-all">
    854. 

  854.   <div id="conjugate,Complex[T]">
    855. 

  855.   <dt><pre><span class="Keyword">func</span> <a href="#conjugate%2CComplex%5BT%5D"><span class="Identifier">conjugate</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    856. 

  856.   <dd>
    857. 

  857.     
    858. 

  858.     Returns the complex conjugate of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt> (<tt class="docutils literal"><span class="pre"><span class="Identifier">complex</span><span class="Punctuation">(</span><span class="Identifier">z</span><span class="Operator">.</span><span class="Identifier">re</span><span class="Punctuation">,</span> <span class="Operator">-</span><span class="Identifier">z</span><span class="Operator">.</span><span class="Identifier">im</span><span class="Punctuation">)</span></span></tt>).
    859. 

  859.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L88" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    860. 

  860. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L88" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    861. 

  861. 

  862.   </dd>
    863. 

  863. </div>
    864. 

  864. 

  865. </div>
    866. 

  866. <div id="cos-procs-all">
    867. 

  867.   <div id="cos,Complex[T]">
    868. 

  868.   <dt><pre><span class="Keyword">func</span> <a href="#cos%2CComplex%5BT%5D"><span class="Identifier">cos</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    869. 

  869.   <dd>
    870. 

  870.     
    871. 

  871.     Returns the cosine of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
    872. 

  872.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L275" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    873. 

  873. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L275" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    874. 

  874. 

  875.   </dd>
    876. 

  876. </div>
    877. 

  877. 

  878. </div>
    879. 

  879. <div id="cosh-procs-all">
    880. 

  880.   <div id="cosh,Complex[T]">
    881. 

  881.   <dt><pre><span class="Keyword">func</span> <a href="#cosh%2CComplex%5BT%5D"><span class="Identifier">cosh</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    882. 

  882.   <dd>
    883. 

  883.     
    884. 

  884.     Returns the hyperbolic cosine of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
    885. 

  885.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L325" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    886. 

  886. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L325" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    887. 

  887. 

  888.   </dd>
    889. 

  889. </div>
    890. 

  890. 

  891. </div>
    892. 

  892. <div id="cot-procs-all">
    893. 

  893.   <div id="cot,Complex[T]">
    894. 

  894.   <dt><pre><span class="Keyword">func</span> <a href="#cot%2CComplex%5BT%5D"><span class="Identifier">cot</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    895. 

  895.   <dd>
    896. 

  896.     
    897. 

  897.     Returns the cotangent of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
    898. 

  898.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L293" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    899. 

  899. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L293" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    900. 

  900. 

  901.   </dd>
    902. 

  902. </div>
    903. 

  903. 

  904. </div>
    905. 

  905. <div id="coth-procs-all">
    906. 

  906.   <div id="coth,Complex[T]">
    907. 

  907.   <dt><pre><span class="Keyword">func</span> <a href="#coth%2CComplex%5BT%5D"><span class="Identifier">coth</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    908. 

  908.   <dd>
    909. 

  909.     
    910. 

  910.     Returns the hyperbolic cotangent of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
    911. 

  911.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L341" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    912. 

  912. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L341" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    913. 

  913. 

  914.   </dd>
    915. 

  915. </div>
    916. 

  916. 

  917. </div>
    918. 

  918. <div id="csc-procs-all">
    919. 

  919.   <div id="csc,Complex[T]">
    920. 

  920.   <dt><pre><span class="Keyword">func</span> <a href="#csc%2CComplex%5BT%5D"><span class="Identifier">csc</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    921. 

  921.   <dd>
    922. 

  922.     
    923. 

  923.     Returns the cosecant of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
    924. 

  924.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L309" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    925. 

  925. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L309" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    926. 

  926. 

  927.   </dd>
    928. 

  928. </div>
    929. 

  929. 

  930. </div>
    931. 

  931. <div id="csch-procs-all">
    932. 

  932.   <div id="csch,Complex[T]">
    933. 

  933.   <dt><pre><span class="Keyword">func</span> <a href="#csch%2CComplex%5BT%5D"><span class="Identifier">csch</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    934. 

  934.   <dd>
    935. 

  935.     
    936. 

  936.     Returns the hyperbolic cosecant of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
    937. 

  937.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L357" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    938. 

  938. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L357" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    939. 

  939. 

  940.   </dd>
    941. 

  941. </div>
    942. 

  942. 

  943. </div>
    944. 

  944. <div id="exp-procs-all">
    945. 

  945.   <div id="exp,Complex[T]">
    946. 

  946.   <dt><pre><span class="Keyword">func</span> <a href="#exp%2CComplex%5BT%5D"><span class="Identifier">exp</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    947. 

  947.   <dd>
    948. 

  948.     
    949. 

  949.     Computes the exponential function (<tt class="docutils literal"><span class="pre"><span class="Identifier">e</span><span class="Operator">^</span><span class="Identifier">z</span></span></tt>).
    950. 

  950.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L198" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    951. 

  951. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L198" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    952. 

  952. 

  953.   </dd>
    954. 

  954. </div>
    955. 

  955. 

  956. </div>
    957. 

  957. <div id="formatValue-procs-all">
    958. 

  958.   <div id="formatValue,string,Complex,string">
    959. 

  959.   <dt><pre><span class="Keyword">proc</span> <a href="#formatValue%2Cstring%2CComplex%2Cstring"><span class="Identifier">formatValue</span></a><span class="Other">(</span><span class="Identifier">result</span><span class="Other">:</span> <span class="Keyword">var</span> <a href="system.html#string"><span class="Identifier">string</span></a><span class="Other">;</span> <span class="Identifier">value</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">;</span> <span class="Identifier">specifier</span><span class="Other">:</span> <a href="system.html#string"><span class="Identifier">string</span></a><span class="Other">)</span></pre></dt>
    960. 

  960.   <dd>
    961. 

  961.     
    962. 

  962.     Standard format implementation for <tt class="docutils literal"><span class="pre"><span class="Identifier">Complex</span></span></tt>. It makes little sense to call this directly, but it is required to exist by the <tt class="docutils literal"><span class="pre"><span class="Operator">&amp;</span></span></tt> macro. For complex numbers, we add a specific 'j' specifier, which formats the value as (A+Bj) like in mathematics.
    963. 

  963.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L439" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    964. 

  964. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L439" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    965. 

  965. 

  966.   </dd>
    967. 

  967. </div>
    968. 

  968. 

  969. </div>
    970. 

  970. <div id="inv-procs-all">
    971. 

  971.   <div id="inv,Complex[T]">
    972. 

  972.   <dt><pre><span class="Keyword">func</span> <a href="#inv%2CComplex%5BT%5D"><span class="Identifier">inv</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    973. 

  973.   <dd>
    974. 

  974.     
    975. 

  975.     Returns the multiplicative inverse of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt> (<tt class="docutils literal"><span class="pre"><span class="DecNumber">1</span><span class="Operator">/</span><span class="Identifier">z</span></span></tt>).
    976. 

  976.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L92" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    977. 

  977. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L92" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    978. 

  978. 

  979.   </dd>
    980. 

  980. </div>
    981. 

  981. 

  982. </div>
    983. 

  983. <div id="ln-procs-all">
    984. 

  984.   <div id="ln,Complex[T]">
    985. 

  985.   <dt><pre><span class="Keyword">func</span> <a href="#ln%2CComplex%5BT%5D"><span class="Identifier">ln</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    986. 

  986.   <dd>
    987. 

  987.     
    988. 

  988.     Returns the (<a class="reference external" href="https://en.wikipedia.org/wiki/Complex_logarithm#Principal_value">principal value</a> of the) natural logarithm of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
    989. 

  989.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L205" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    990. 

  990. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L205" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    991. 

  991. 

  992.   </dd>
    993. 

  993. </div>
    994. 

  994. 

  995. </div>
    996. 

  996. <div id="log2-procs-all">
    997. 

  997.   <div id="log2,Complex[T]">
    998. 

  998.   <dt><pre><span class="Keyword">func</span> <a href="#log2%2CComplex%5BT%5D"><span class="Identifier">log2</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    999. 

  999.   <dd>
    1000. 

  1000.     
    1001. 

  1001.     <p>Returns the logarithm base 2 of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.</p>
    1002. 

  1002. <p><strong>See also:</strong></p>
    1003. 

  1003. <ul class="simple"><li><a class="reference external" href="#ln,Complex[T]">ln func</a></li>
    1004. 

  1004. </ul>
    1005. 

  1005. 

  1006.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L218" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1007. 

  1007. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L218" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1008. 

  1008. 

  1009.   </dd>
    1010. 

  1010. </div>
    1011. 

  1011. 

  1012. </div>
    1013. 

  1013. <div id="log10-procs-all">
    1014. 

  1014.   <div id="log10,Complex[T]">
    1015. 

  1015.   <dt><pre><span class="Keyword">func</span> <a href="#log10%2CComplex%5BT%5D"><span class="Identifier">log10</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    1016. 

  1016.   <dd>
    1017. 

  1017.     
    1018. 

  1018.     <p>Returns the logarithm base 10 of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.</p>
    1019. 

  1019. <p><strong>See also:</strong></p>
    1020. 

  1020. <ul class="simple"><li><a class="reference external" href="#ln,Complex[T]">ln func</a></li>
    1021. 

  1021. </ul>
    1022. 

  1022. 

  1023.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L211" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1024. 

  1024. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L211" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1025. 

  1025. 

  1026.   </dd>
    1027. 

  1027. </div>
    1028. 

  1028. 

  1029. </div>
    1030. 

  1030. <div id="phase-procs-all">
    1031. 

  1031.   <div id="phase,Complex[T]">
    1032. 

  1032.   <dt><pre><span class="Keyword">func</span> <a href="#phase%2CComplex%5BT%5D"><span class="Identifier">phase</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">T</span></pre></dt>
    1033. 

  1033.   <dd>
    1034. 

  1034.     
    1035. 

  1035.     Returns the phase (or argument) of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>, that is the angle in polar representation.<p><tt class="docutils literal"><span class="pre"><span class="Identifier">result</span> <span class="Operator">=</span> <span class="Identifier">arctan2</span><span class="Punctuation">(</span><span class="Identifier">z</span><span class="Operator">.</span><span class="Identifier">im</span><span class="Punctuation">,</span> <span class="Identifier">z</span><span class="Operator">.</span><span class="Identifier">re</span><span class="Punctuation">)</span></span></tt><br/></p>
    1036. 

  1036.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L365" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1037. 

  1037. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L365" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1038. 

  1038. 

  1039.   </dd>
    1040. 

  1040. </div>
    1041. 

  1041. 

  1042. </div>
    1043. 

  1043. <div id="polar-procs-all">
    1044. 

  1044.   <div id="polar,Complex[T]">
    1045. 

  1045.   <dt><pre><span class="Keyword">func</span> <a href="#polar%2CComplex%5BT%5D"><span class="Identifier">polar</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <span class="Keyword">tuple</span><span class="Other">[</span><span class="Identifier">r</span><span class="Other">,</span> <span class="Identifier">phi</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    1046. 

  1046.   <dd>
    1047. 

  1047.     
    1048. 

  1048.     Returns <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt> in polar coordinates.<p><tt class="docutils literal"><span class="pre"><span class="Identifier">result</span><span class="Operator">.</span><span class="Identifier">r</span> <span class="Operator">=</span> <span class="Identifier">abs</span><span class="Punctuation">(</span><span class="Identifier">z</span><span class="Punctuation">)</span></span></tt><br/><tt class="docutils literal"><span class="pre"><span class="Identifier">result</span><span class="Operator">.</span><span class="Identifier">phi</span> <span class="Operator">=</span> <span class="Identifier">phase</span><span class="Punctuation">(</span><span class="Identifier">z</span><span class="Punctuation">)</span></span></tt><br/></p><p><strong>See also:</strong></p>
    1049. 

  1049. <ul class="simple"><li><a class="reference external" href="#rect,T,T">rect func</a> for the inverse operation</li>
    1050. 

  1050. </ul>
    1051. 

  1051. 

  1052.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L371" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1053. 

  1053. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L371" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1054. 

  1054. 

  1055.   </dd>
    1056. 

  1056. </div>
    1057. 

  1057. 

  1058. </div>
    1059. 

  1059. <div id="pow-procs-all">
    1060. 

  1060.   <div id="pow,Complex[T],Complex[T]">
    1061. 

  1061.   <dt><pre><span class="Keyword">func</span> <a href="#pow%2CComplex%5BT%5D%2CComplex%5BT%5D"><span class="Identifier">pow</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">,</span> <span class="Identifier">y</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    1062. 

  1062.   <dd>
    1063. 

  1063.     
    1064. 

  1064.     <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> raised to the power of <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.
    1065. 

  1065.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L225" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1066. 

  1066. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L225" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1067. 

  1067. 

  1068.   </dd>
    1069. 

  1069. </div>
    1070. 

  1070. <div id="pow,Complex[T],T">
    1071. 

  1071.   <dt><pre><span class="Keyword">func</span> <a href="#pow%2CComplex%5BT%5D%2CT"><span class="Identifier">pow</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">x</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">y</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    1072. 

  1072.   <dd>
    1073. 

  1073.     
    1074. 

  1074.     The complex number <tt class="docutils literal"><span class="pre"><span class="Identifier">x</span></span></tt> raised to the power of the real number <tt class="docutils literal"><span class="pre"><span class="Identifier">y</span></span></tt>.
    1075. 

  1075.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L263" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1076. 

  1076. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L263" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1077. 

  1077. 

  1078.   </dd>
    1079. 

  1079. </div>
    1080. 

  1080. 

  1081. </div>
    1082. 

  1082. <div id="rect-procs-all">
    1083. 

  1083.   <div id="rect,T,T">
    1084. 

  1084.   <dt><pre><span class="Keyword">func</span> <a href="#rect%2CT%2CT"><span class="Identifier">rect</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">r</span><span class="Other">,</span> <span class="Identifier">phi</span><span class="Other">:</span> <span class="Identifier">T</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    1085. 

  1085.   <dd>
    1086. 

  1086.     
    1087. 

  1087.     Returns the complex number with polar coordinates <tt class="docutils literal"><span class="pre"><span class="Identifier">r</span></span></tt> and <tt class="docutils literal"><span class="pre"><span class="Identifier">phi</span></span></tt>.<p><tt class="docutils literal"><span class="pre"><span class="Identifier">result</span><span class="Operator">.</span><span class="Identifier">re</span> <span class="Operator">=</span> <span class="Identifier">r</span> <span class="Operator">*</span> <span class="Identifier">cos</span><span class="Punctuation">(</span><span class="Identifier">phi</span><span class="Punctuation">)</span></span></tt><br/><tt class="docutils literal"><span class="pre"><span class="Identifier">result</span><span class="Operator">.</span><span class="Identifier">im</span> <span class="Operator">=</span> <span class="Identifier">r</span> <span class="Operator">*</span> <span class="Identifier">sin</span><span class="Punctuation">(</span><span class="Identifier">phi</span><span class="Punctuation">)</span></span></tt><br/></p><p><strong>See also:</strong></p>
    1088. 

  1088. <ul class="simple"><li><a class="reference external" href="#polar,Complex[T]">polar func</a> for the inverse operation</li>
    1089. 

  1089. </ul>
    1090. 

  1090. 

  1091.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L381" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1092. 

  1092. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L381" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1093. 

  1093. 

  1094.   </dd>
    1095. 

  1095. </div>
    1096. 

  1096. 

  1097. </div>
    1098. 

  1098. <div id="sec-procs-all">
    1099. 

  1099.   <div id="sec,Complex[T]">
    1100. 

  1100.   <dt><pre><span class="Keyword">func</span> <a href="#sec%2CComplex%5BT%5D"><span class="Identifier">sec</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    1101. 

  1101.   <dd>
    1102. 

  1102.     
    1103. 

  1103.     Returns the secant of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
    1104. 

  1104.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L301" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1105. 

  1105. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L301" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1106. 

  1106. 

  1107.   </dd>
    1108. 

  1108. </div>
    1109. 

  1109. 

  1110. </div>
    1111. 

  1111. <div id="sech-procs-all">
    1112. 

  1112.   <div id="sech,Complex[T]">
    1113. 

  1113.   <dt><pre><span class="Keyword">func</span> <a href="#sech%2CComplex%5BT%5D"><span class="Identifier">sech</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    1114. 

  1114.   <dd>
    1115. 

  1115.     
    1116. 

  1116.     Returns the hyperbolic secant of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
    1117. 

  1117.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L349" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1118. 

  1118. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L349" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1119. 

  1119. 

  1120.   </dd>
    1121. 

  1121. </div>
    1122. 

  1122. 

  1123. </div>
    1124. 

  1124. <div id="sgn-procs-all">
    1125. 

  1125.   <div id="sgn,Complex[T]">
    1126. 

  1126.   <dt><pre><span class="Keyword">func</span> <a href="#sgn%2CComplex%5BT%5D"><span class="Identifier">sgn</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    1127. 

  1127.   <dd>
    1128. 

  1128.     
    1129. 

  1129.     Returns the phase of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt> as a unit complex number, or 0 if <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt> is 0.
    1130. 

  1130.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L79" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1131. 

  1131. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L79" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1132. 

  1132. 

  1133.   </dd>
    1134. 

  1134. </div>
    1135. 

  1135. 

  1136. </div>
    1137. 

  1137. <div id="sin-procs-all">
    1138. 

  1138.   <div id="sin,Complex[T]">
    1139. 

  1139.   <dt><pre><span class="Keyword">func</span> <a href="#sin%2CComplex%5BT%5D"><span class="Identifier">sin</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    1140. 

  1140.   <dd>
    1141. 

  1141.     
    1142. 

  1142.     Returns the sine of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
    1143. 

  1143.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L267" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1144. 

  1144. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L267" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1145. 

  1145. 

  1146.   </dd>
    1147. 

  1147. </div>
    1148. 

  1148. 

  1149. </div>
    1150. 

  1150. <div id="sinh-procs-all">
    1151. 

  1151.   <div id="sinh,Complex[T]">
    1152. 

  1152.   <dt><pre><span class="Keyword">func</span> <a href="#sinh%2CComplex%5BT%5D"><span class="Identifier">sinh</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    1153. 

  1153.   <dd>
    1154. 

  1154.     
    1155. 

  1155.     Returns the hyperbolic sine of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
    1156. 

  1156.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L317" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1157. 

  1157. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L317" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1158. 

  1158. 

  1159.   </dd>
    1160. 

  1160. </div>
    1161. 

  1161. 

  1162. </div>
    1163. 

  1163. <div id="sqrt-procs-all">
    1164. 

  1164.   <div id="sqrt,Complex[T]">
    1165. 

  1165.   <dt><pre><span class="Keyword">func</span> <a href="#sqrt%2CComplex%5BT%5D"><span class="Identifier">sqrt</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    1166. 

  1166.   <dd>
    1167. 

  1167.     
    1168. 

  1168.     Computes the (<a class="reference external" href="https://en.wikipedia.org/wiki/Square_root#Principal_square_root_of_a_complex_number">principal</a>) square root of a complex number <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
    1169. 

  1169.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L174" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1170. 

  1170. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L174" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1171. 

  1171. 

  1172.   </dd>
    1173. 

  1173. </div>
    1174. 

  1174. 

  1175. </div>
    1176. 

  1176. <div id="tan-procs-all">
    1177. 

  1177.   <div id="tan,Complex[T]">
    1178. 

  1178.   <dt><pre><span class="Keyword">func</span> <a href="#tan%2CComplex%5BT%5D"><span class="Identifier">tan</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    1179. 

  1179.   <dd>
    1180. 

  1180.     
    1181. 

  1181.     Returns the tangent of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
    1182. 

  1182.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L285" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1183. 

  1183. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L285" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1184. 

  1184. 

  1185.   </dd>
    1186. 

  1186. </div>
    1187. 

  1187. 

  1188. </div>
    1189. 

  1189. <div id="tanh-procs-all">
    1190. 

  1190.   <div id="tanh,Complex[T]">
    1191. 

  1191.   <dt><pre><span class="Keyword">func</span> <a href="#tanh%2CComplex%5BT%5D"><span class="Identifier">tanh</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">z</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex"><span class="Identifier">Complex</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
    1192. 

  1192.   <dd>
    1193. 

  1193.     
    1194. 

  1194.     Returns the hyperbolic tangent of <tt class="docutils literal"><span class="pre"><span class="Identifier">z</span></span></tt>.
    1195. 

  1195.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L333" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1196. 

  1196. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L333" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1197. 

  1197. 

  1198.   </dd>
    1199. 

  1199. </div>
    1200. 

  1200. 

  1201. </div>
    1202. 

  1202. 

  1203.   </dl>
    1204. 

  1204. </div>
    1205. 

  1205. <div class="section" id="18">
    1206. 

  1206.   <h1><a class="toc-backref" href="#18">Templates</a></h1>
    1207. 

  1207.   <dl class="item">
    1208. 

  1208.     <div id="im-templates-all">
    1209. 

  1209.   <div id="im.t,float32">
    1210. 

  1210.   <dt><pre><span class="Keyword">template</span> <a href="#im.t%2Cfloat32"><span class="Identifier">im</span></a><span class="Other">(</span><span class="Identifier">arg</span><span class="Other">:</span> <a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex32"><span class="Identifier">Complex32</span></a></pre></dt>
    1211. 

  1211.   <dd>
    1212. 

  1212.     
    1213. 

  1213.     Returns <tt class="docutils literal"><span class="pre"><span class="Identifier">arg</span></span></tt> as an imaginary number (<tt class="docutils literal"><span class="pre"><span class="Identifier">complex32</span><span class="Punctuation">(</span><span class="DecNumber">0</span><span class="Punctuation">,</span> <span class="Identifier">arg</span><span class="Punctuation">)</span></span></tt>).
    1214. 

  1214.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L63" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1215. 

  1215. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L63" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1216. 

  1216. 

  1217.   </dd>
    1218. 

  1218. </div>
    1219. 

  1219. <div id="im.t,float64">
    1220. 

  1220.   <dt><pre><span class="Keyword">template</span> <a href="#im.t%2Cfloat64"><span class="Identifier">im</span></a><span class="Other">(</span><span class="Identifier">arg</span><span class="Other">:</span> <a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex64"><span class="Identifier">Complex64</span></a></pre></dt>
    1221. 

  1221.   <dd>
    1222. 

  1222.     
    1223. 

  1223.     Returns <tt class="docutils literal"><span class="pre"><span class="Identifier">arg</span></span></tt> as an imaginary number (<tt class="docutils literal"><span class="pre"><span class="Identifier">complex64</span><span class="Punctuation">(</span><span class="DecNumber">0</span><span class="Punctuation">,</span> <span class="Identifier">arg</span><span class="Punctuation">)</span></span></tt>).
    1224. 

  1224.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L65" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1225. 

  1225. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L65" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1226. 

  1226. 

  1227.   </dd>
    1228. 

  1228. </div>
    1229. 

  1229. <div id="im.t,typedesc[float32]">
    1230. 

  1230.   <dt><pre><span class="Keyword">template</span> <a href="#im.t%2Ctypedesc%5Bfloat32%5D"><span class="Identifier">im</span></a><span class="Other">(</span><span class="Identifier">arg</span><span class="Other">:</span> <a href="system.html#typedesc"><span class="Identifier">typedesc</span></a><span class="Other">[</span><a href="system.html#float32"><span class="Identifier">float32</span></a><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex32"><span class="Identifier">Complex32</span></a></pre></dt>
    1231. 

  1231.   <dd>
    1232. 

  1232.     
    1233. 

  1233.     Returns the imaginary unit (<tt class="docutils literal"><span class="pre"><span class="Identifier">complex32</span><span class="Punctuation">(</span><span class="DecNumber">0</span><span class="Punctuation">,</span> <span class="DecNumber">1</span><span class="Punctuation">)</span></span></tt>).
    1234. 

  1234.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L59" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1235. 

  1235. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L59" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1236. 

  1236. 

  1237.   </dd>
    1238. 

  1238. </div>
    1239. 

  1239. <div id="im.t,typedesc[float64]">
    1240. 

  1240.   <dt><pre><span class="Keyword">template</span> <a href="#im.t%2Ctypedesc%5Bfloat64%5D"><span class="Identifier">im</span></a><span class="Other">(</span><span class="Identifier">arg</span><span class="Other">:</span> <a href="system.html#typedesc"><span class="Identifier">typedesc</span></a><span class="Other">[</span><a href="system.html#float64"><span class="Identifier">float64</span></a><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="complex.html#Complex64"><span class="Identifier">Complex64</span></a></pre></dt>
    1241. 

  1241.   <dd>
    1242. 

  1242.     
    1243. 

  1243.     Returns the imaginary unit (<tt class="docutils literal"><span class="pre"><span class="Identifier">complex64</span><span class="Punctuation">(</span><span class="DecNumber">0</span><span class="Punctuation">,</span> <span class="DecNumber">1</span><span class="Punctuation">)</span></span></tt>).
    1244. 

  1244.     <a href="https://github.com/nim-lang/Nim/tree/devel/lib/pure/complex.nim#L61" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
    1245. 

  1245. <a href="https://github.com/nim-lang/Nim/edit/devel/lib/pure/complex.nim#L61" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;
    1246. 

  1246. 

  1247.   </dd>
    1248. 

  1248. </div>
    1249. 

  1249. 

  1250. </div>
    1251. 

  1251. 

  1252.   </dl>
    1253. 

  1253. </div>
    1254. 

  1254. 

  1255.   </div>
    1256. 

  1256. </div>
    1257. 

  1257. 

  1258.       <div class="twelve-columns footer">
    1259. 

  1259.         <span class="nim-sprite"></span>
    1260. 

  1260.         <br>
    1261. 

  1261.         <small style="color: var(--hint);">Made with Nim. Generated: 2025-03-15 14:13:19 UTC</small>
    1262. 

  1262.       </div>
    1263. 

  1263.     </div>
    1264. 

  1264.   </div>
    1265. 

  1265.       <script defer data-domain="nim-lang.org" src="https://plausible.io/js/plausible.js"></script>
    1266. 

  1266.     
    1267. 

  1267. </body>
    1268. 

  1268. </html>
    1269. 

  1269.