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<html xmlns="http://www.w3.org/1999/xhtml"><head><title>Complex (ocaml.Stdlib.Complex)</title><link rel="stylesheet" href="../../../_odoc-theme/odoc.css"/><meta charset="utf-8"/><meta name="generator" content="odoc 2.2.1"/><meta name="viewport" content="width=device-width,initial-scale=1.0"/><script src="../../../highlight.pack.js"></script><script>hljs.initHighlightingOnLoad();</script></head><body class="odoc"><nav class="odoc-nav"><a href="../index.html">Up</a> <a href="../../index.html">ocaml</a> &#x00BB; <a href="../index.html">Stdlib</a> &#x00BB; Complex</nav><header class="odoc-preamble"><h1>Module <code><span>Stdlib.Complex</span></code></h1><p>Complex numbers.</p><p>This module provides arithmetic operations on complex numbers. Complex numbers are represented by their real and imaginary parts (cartesian representation). Each part is represented by a double-precision floating-point number (type <code>float</code>).</p></header><div class="odoc-content"><div class="odoc-spec"><div class="spec type anchored" id="type-t"><a href="#type-t" class="anchor"></a><code><span><span class="keyword">type</span> t</span><span> = </span><span>{</span></code><ol><li id="type-t.re" class="def record field anchored"><a href="#type-t.re" class="anchor"></a><code><span>re : float;</span></code></li><li id="type-t.im" class="def record field anchored"><a href="#type-t.im" class="anchor"></a><code><span>im : float;</span></code></li></ol><code><span>}</span></code></div><div class="spec-doc"><p>The type of complex numbers. <code>re</code> is the real part and <code>im</code> the imaginary part.</p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-zero"><a href="#val-zero" class="anchor"></a><code><span><span class="keyword">val</span> zero : <a href="#type-t">t</a></span></code></div><div class="spec-doc"><p>The complex number <code>0</code>.</p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-one"><a href="#val-one" class="anchor"></a><code><span><span class="keyword">val</span> one : <a href="#type-t">t</a></span></code></div><div class="spec-doc"><p>The complex number <code>1</code>.</p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-i"><a href="#val-i" class="anchor"></a><code><span><span class="keyword">val</span> i : <a href="#type-t">t</a></span></code></div><div class="spec-doc"><p>The complex number <code>i</code>.</p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-neg"><a href="#val-neg" class="anchor"></a><code><span><span class="keyword">val</span> neg : <span><a href="#type-t">t</a> <span class="arrow">&#45;&gt;</span></span> <a href="#type-t">t</a></span></code></div><div class="spec-doc"><p>Unary negation.</p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-conj"><a href="#val-conj" class="anchor"></a><code><span><span class="keyword">val</span> conj : <span><a href="#type-t">t</a> <span class="arrow">&#45;&gt;</span></span> <a href="#type-t">t</a></span></code></div><div class="spec-doc"><p>Conjugate: given the complex <code>x + i.y</code>, returns <code>x - i.y</code>.</p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-add"><a href="#val-add" class="anchor"></a><code><span><span class="keyword">val</span> add : <span><a href="#type-t">t</a> <span class="arrow">&#45;&gt;</span></span> <span><a href="#type-t">t</a> <span class="arrow">&#45;&gt;</span></span> <a href="#type-t">t</a></span></code></div><div class="spec-doc"><p>Addition</p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-sub"><a href="#val-sub" class="anchor"></a><code><span><span class="keyword">val</span> sub : <span><a href="#type-t">t</a> <span class="arrow">&#45;&gt;</span></span> <span><a href="#type-t">t</a> <span class="arrow">&#45;&gt;</span></span> <a href="#type-t">t</a></span></code></div><div class="spec-doc"><p>Subtraction</p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-mul"><a href="#val-mul" class="anchor"></a><code><span><span class="keyword">val</span> mul : <span><a href="#type-t">t</a> <span class="arrow">&#45;&gt;</span></span> <span><a href="#type-t">t</a> <span class="arrow">&#45;&gt;</span></span> <a href="#type-t">t</a></span></code></div><div class="spec-doc"><p>Multiplication</p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-inv"><a href="#val-inv" class="anchor"></a><code><span><span class="keyword">val</span> inv : <span><a href="#type-t">t</a> <span class="arrow">&#45;&gt;</span></span> <a href="#type-t">t</a></span></code></div><div class="spec-doc"><p>Multiplicative inverse (<code>1/z</code>).</p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-div"><a href="#val-div" class="anchor"></a><code><span><span class="keyword">val</span> div : <span><a href="#type-t">t</a> <span class="arrow">&#45;&gt;</span></span> <span><a href="#type-t">t</a> <span class="arrow">&#45;&gt;</span></span> <a href="#type-t">t</a></span></code></div><div class="spec-doc"><p>Division</p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-sqrt"><a href="#val-sqrt" class="anchor"></a><code><span><span class="keyword">val</span> sqrt : <span><a href="#type-t">t</a> <span class="arrow">&#45;&gt;</span></span> <a href="#type-t">t</a></span></code></div><div class="spec-doc"><p>Square root. The result <code>x + i.y</code> is such that <code>x &gt; 0</code> or <code>x = 0</code> and <code>y &gt;= 0</code>. This function has a discontinuity along the negative real axis.</p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-norm2"><a href="#val-norm2" class="anchor"></a><code><span><span class="keyword">val</span> norm2 : <span><a href="#type-t">t</a> <span class="arrow">&#45;&gt;</span></span> float</span></code></div><div class="spec-doc"><p>Norm squared: given <code>x + i.y</code>, returns <code>x^2 + y^2</code>.</p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-norm"><a href="#val-norm" class="anchor"></a><code><span><span class="keyword">val</span> norm : <span><a href="#type-t">t</a> <span class="arrow">&#45;&gt;</span></span> float</span></code></div><div class="spec-doc"><p>Norm: given <code>x + i.y</code>, returns <code>sqrt(x^2 + y^2)</code>.</p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-arg"><a href="#val-arg" class="anchor"></a><code><span><span class="keyword">val</span> arg : <span><a href="#type-t">t</a> <span class="arrow">&#45;&gt;</span></span> float</span></code></div><div class="spec-doc"><p>Argument. The argument of a complex number is the angle in the complex plane between the positive real axis and a line passing through zero and the number. This angle ranges from <code>-pi</code> to <code>pi</code>. This function has a discontinuity along the negative real axis.</p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-polar"><a href="#val-polar" class="anchor"></a><code><span><span class="keyword">val</span> polar : <span>float <span class="arrow">&#45;&gt;</span></span> <span>float <span class="arrow">&#45;&gt;</span></span> <a href="#type-t">t</a></span></code></div><div class="spec-doc"><p><code>polar norm arg</code> returns the complex having norm <code>norm</code> and argument <code>arg</code>.</p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-exp"><a href="#val-exp" class="anchor"></a><code><span><span class="keyword">val</span> exp : <span><a href="#type-t">t</a> <span class="arrow">&#45;&gt;</span></span> <a href="#type-t">t</a></span></code></div><div class="spec-doc"><p>Exponentiation. <code>exp z</code> returns <code>e</code> to the <code>z</code> power.</p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-log"><a href="#val-log" class="anchor"></a><code><span><span class="keyword">val</span> log : <span><a href="#type-t">t</a> <span class="arrow">&#45;&gt;</span></span> <a href="#type-t">t</a></span></code></div><div class="spec-doc"><p>Natural logarithm (in base <code>e</code>).</p></div></div><div class="odoc-spec"><div class="spec value anchored" id="val-pow"><a href="#val-pow" class="anchor"></a><code><span><span class="keyword">val</span> pow : <span><a href="#type-t">t</a> <span class="arrow">&#45;&gt;</span></span> <span><a href="#type-t">t</a> <span class="arrow">&#45;&gt;</span></span> <a href="#type-t">t</a></span></code></div><div class="spec-doc"><p>Power function. <code>pow z1 z2</code> returns <code>z1</code> to the <code>z2</code> power.</p></div></div></div></body></html>