<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Data.Complex</title><link href="ocean.css" rel="stylesheet" type="text/css" title="Ocean" /><script src="haddock-util.js" type="text/javascript"></script><script type="text/javascript">//<![CDATA[
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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="index.html">Contents</a></li><li><a href="doc-index.html">Index</a></li></ul><p class="caption">base-4.5.1.0: Basic libraries</p></div><div id="content"><div id="module-header"><table class="info"><tr><th>Portability</th><td>portable</td></tr><tr><th>Stability</th><td>provisional</td></tr><tr><th>Maintainer</th><td>libraries@haskell.org</td></tr><tr><th>Safe Haskell</th><td>Trustworthy</td></tr></table><p class="caption">Data.Complex</p></div><div id="table-of-contents"><p class="caption">Contents</p><ul><li><a href="#g:1">Rectangular form
</a></li><li><a href="#g:2">Polar form
</a></li><li><a href="#g:3">Conjugate
</a></li></ul></div><div id="description"><p class="caption">Description</p><div class="doc"><p>Complex numbers.
</p></div></div><div id="synopsis"><p id="control.syn" class="caption expander" onclick="toggleSection('syn')">Synopsis</p><ul id="section.syn" class="hide" onclick="toggleSection('syn')"><li class="src short"><span class="keyword">data</span> <a href="#t:Complex">Complex</a> a = !a <a href="#v::-43-">:+</a> !a</li><li class="src short"><a href="#v:realPart">realPart</a> :: <a href="Prelude.html#t:RealFloat">RealFloat</a> a => <a href="Data-Complex.html#t:Complex">Complex</a> a -> a</li><li class="src short"><a href="#v:imagPart">imagPart</a> :: <a href="Prelude.html#t:RealFloat">RealFloat</a> a => <a href="Data-Complex.html#t:Complex">Complex</a> a -> a</li><li class="src short"><a href="#v:mkPolar">mkPolar</a> :: <a href="Prelude.html#t:RealFloat">RealFloat</a> a => a -> a -> <a href="Data-Complex.html#t:Complex">Complex</a> a</li><li class="src short"><a href="#v:cis">cis</a> :: <a href="Prelude.html#t:RealFloat">RealFloat</a> a => a -> <a href="Data-Complex.html#t:Complex">Complex</a> a</li><li class="src short"><a href="#v:polar">polar</a> :: <a href="Prelude.html#t:RealFloat">RealFloat</a> a => <a href="Data-Complex.html#t:Complex">Complex</a> a -> (a, a)</li><li class="src short"><a href="#v:magnitude">magnitude</a> :: <a href="Prelude.html#t:RealFloat">RealFloat</a> a => <a href="Data-Complex.html#t:Complex">Complex</a> a -> a</li><li class="src short"><a href="#v:phase">phase</a> :: <a href="Prelude.html#t:RealFloat">RealFloat</a> a => <a href="Data-Complex.html#t:Complex">Complex</a> a -> a</li><li class="src short"><a href="#v:conjugate">conjugate</a> :: <a href="Prelude.html#t:RealFloat">RealFloat</a> a => <a href="Data-Complex.html#t:Complex">Complex</a> a -> <a href="Data-Complex.html#t:Complex">Complex</a> a</li></ul></div><div id="interface"><h1 id="g:1">Rectangular form
</h1><div class="top"><p class="src"><span class="keyword">data</span> <a name="t:Complex" class="def">Complex</a> a </p><div class="doc"><p>Complex numbers are an algebraic type.
</p><p>For a complex number <code>z</code>, <code><code><a href="Prelude.html#v:abs">abs</a></code> z</code> is a number with the magnitude of <code>z</code>,
but oriented in the positive real direction, whereas <code><code><a href="Prelude.html#v:signum">signum</a></code> z</code>
has the phase of <code>z</code>, but unit magnitude.
</p></div><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src">!a <a name="v::-43-" class="def">:+</a> !a</td><td class="doc"><p>forms a complex number from its real and imaginary
rectangular components.
</p></td></tr></table></div><div class="subs instances"><p id="control.i:Complex" class="caption collapser" onclick="toggleSection('i:Complex')">Instances</p><div id="section.i:Complex" class="show"><table><tr><td class="src"><a href="Data-Typeable-Internal.html#t:Typeable1">Typeable1</a> <a href="Data-Complex.html#t:Complex">Complex</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-Eq.html#t:Eq">Eq</a> a => <a href="Data-Eq.html#t:Eq">Eq</a> (<a href="Data-Complex.html#t:Complex">Complex</a> a)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Prelude.html#t:RealFloat">RealFloat</a> a => <a href="Prelude.html#t:Floating">Floating</a> (<a href="Data-Complex.html#t:Complex">Complex</a> a)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Prelude.html#t:RealFloat">RealFloat</a> a => <a href="Prelude.html#t:Fractional">Fractional</a> (<a href="Data-Complex.html#t:Complex">Complex</a> a)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-Data.html#t:Data">Data</a> a => <a href="Data-Data.html#t:Data">Data</a> (<a href="Data-Complex.html#t:Complex">Complex</a> a)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Prelude.html#t:RealFloat">RealFloat</a> a => <a href="Prelude.html#t:Num">Num</a> (<a href="Data-Complex.html#t:Complex">Complex</a> a)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Text-Read.html#t:Read">Read</a> a => <a href="Text-Read.html#t:Read">Read</a> (<a href="Data-Complex.html#t:Complex">Complex</a> a)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Text-Show.html#t:Show">Show</a> a => <a href="Text-Show.html#t:Show">Show</a> (<a href="Data-Complex.html#t:Complex">Complex</a> a)</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:realPart" class="def">realPart</a> :: <a href="Prelude.html#t:RealFloat">RealFloat</a> a => <a href="Data-Complex.html#t:Complex">Complex</a> a -> a</p><div class="doc"><p>Extracts the real part of a complex number.
</p></div></div><div class="top"><p class="src"><a name="v:imagPart" class="def">imagPart</a> :: <a href="Prelude.html#t:RealFloat">RealFloat</a> a => <a href="Data-Complex.html#t:Complex">Complex</a> a -> a</p><div class="doc"><p>Extracts the imaginary part of a complex number.
</p></div></div><h1 id="g:2">Polar form
</h1><div class="top"><p class="src"><a name="v:mkPolar" class="def">mkPolar</a> :: <a href="Prelude.html#t:RealFloat">RealFloat</a> a => a -> a -> <a href="Data-Complex.html#t:Complex">Complex</a> a</p><div class="doc"><p>Form a complex number from polar components of magnitude and phase.
</p></div></div><div class="top"><p class="src"><a name="v:cis" class="def">cis</a> :: <a href="Prelude.html#t:RealFloat">RealFloat</a> a => a -> <a href="Data-Complex.html#t:Complex">Complex</a> a</p><div class="doc"><p><code><code><a href="Data-Complex.html#v:cis">cis</a></code> t</code> is a complex value with magnitude <code>1</code>
and phase <code>t</code> (modulo <code>2*<code><a href="Prelude.html#v:pi">pi</a></code></code>).
</p></div></div><div class="top"><p class="src"><a name="v:polar" class="def">polar</a> :: <a href="Prelude.html#t:RealFloat">RealFloat</a> a => <a href="Data-Complex.html#t:Complex">Complex</a> a -> (a, a)</p><div class="doc"><p>The function <code><a href="Data-Complex.html#v:polar">polar</a></code> takes a complex number and
returns a (magnitude, phase) pair in canonical form:
the magnitude is nonnegative, and the phase in the range <code>(-<code><a href="Prelude.html#v:pi">pi</a></code>, <code><a href="Prelude.html#v:pi">pi</a></code>]</code>;
if the magnitude is zero, then so is the phase.
</p></div></div><div class="top"><p class="src"><a name="v:magnitude" class="def">magnitude</a> :: <a href="Prelude.html#t:RealFloat">RealFloat</a> a => <a href="Data-Complex.html#t:Complex">Complex</a> a -> a</p><div class="doc"><p>The nonnegative magnitude of a complex number.
</p></div></div><div class="top"><p class="src"><a name="v:phase" class="def">phase</a> :: <a href="Prelude.html#t:RealFloat">RealFloat</a> a => <a href="Data-Complex.html#t:Complex">Complex</a> a -> a</p><div class="doc"><p>The phase of a complex number, in the range <code>(-<code><a href="Prelude.html#v:pi">pi</a></code>, <code><a href="Prelude.html#v:pi">pi</a></code>]</code>.
If the magnitude is zero, then so is the phase.
</p></div></div><h1 id="g:3">Conjugate
</h1><div class="top"><p class="src"><a name="v:conjugate" class="def">conjugate</a> :: <a href="Prelude.html#t:RealFloat">RealFloat</a> a => <a href="Data-Complex.html#t:Complex">Complex</a> a -> <a href="Data-Complex.html#t:Complex">Complex</a> a</p><div class="doc"><p>The conjugate of a complex number.
</p></div></div></div></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.11.0</p></div></body></html>
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