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<a name="Representation-of-complex-numbers"></a>
<div class="header">
<p>
Next: <a href="Properties-of-complex-numbers.html#Properties-of-complex-numbers" accesskey="n" rel="next">Properties of complex numbers</a>, Up: <a href="Complex-Numbers.html#Complex-Numbers" accesskey="u" rel="up">Complex Numbers</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Representation-of-complex-numbers-1"></a>
<h3 class="section">5.1 Representation of complex numbers</h3>
<a name="index-representations-of-complex-numbers"></a>
<a name="index-polar-form-of-complex-numbers"></a>
<a name="index-gsl_005fcomplex"></a>

<p>Complex numbers are represented using the type <code>gsl_complex</code>. The
internal representation of this type may vary across platforms and
should not be accessed directly. The functions and macros described
below allow complex numbers to be manipulated in a portable way.
</p>
<p>For reference, the default form of the <code>gsl_complex</code> type is
given by the following struct,
</p>
<div class="example">
<pre class="example">typedef struct
{
  double dat[2];
} gsl_complex;
</pre></div>

<p>The real and imaginary part are stored in contiguous elements of a two
element array. This eliminates any padding between the real and
imaginary parts, <code>dat[0]</code> and <code>dat[1]</code>, allowing the struct to
be mapped correctly onto packed complex arrays.
</p>
<dl>
<dt><a name="index-gsl_005fcomplex_005frect"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_rect</strong> <em>(double <var>x</var>, double <var>y</var>)</em></dt>
<dd><p>This function uses the rectangular Cartesian components
(<var>x</var>,<var>y</var>) to return the complex number <em>z = x + i y</em>.  An inline version of this function is used when <code>HAVE_INLINE</code> is defined.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fcomplex_005fpolar"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_polar</strong> <em>(double <var>r</var>, double <var>theta</var>)</em></dt>
<dd><p>This function returns the complex number <em>z = r \exp(i \theta) = r
(\cos(\theta) + i \sin(\theta))</em> from the polar representation
(<var>r</var>,<var>theta</var>).
</p></dd></dl>

<dl>
<dt><a name="index-GSL_005fREAL"></a>Macro: <strong>GSL_REAL</strong> <em>(<var>z</var>)</em></dt>
<dt><a name="index-GSL_005fIMAG"></a>Macro: <strong>GSL_IMAG</strong> <em>(<var>z</var>)</em></dt>
<dd><p>These macros return the real and imaginary parts of the complex number
<var>z</var>.
</p></dd></dl>

<dl>
<dt><a name="index-GSL_005fSET_005fCOMPLEX"></a>Macro: <strong>GSL_SET_COMPLEX</strong> <em>(<var>zp</var>, <var>x</var>, <var>y</var>)</em></dt>
<dd><p>This macro uses the Cartesian components (<var>x</var>,<var>y</var>) to set the
real and imaginary parts of the complex number pointed to by <var>zp</var>.
For example,
</p>
<div class="example">
<pre class="example">GSL_SET_COMPLEX(&amp;z, 3, 4)
</pre></div>

<p>sets <var>z</var> to be <em>3 + 4i</em>.
</p></dd></dl>

<dl>
<dt><a name="index-GSL_005fSET_005fREAL"></a>Macro: <strong>GSL_SET_REAL</strong> <em>(<var>zp</var>,<var>x</var>)</em></dt>
<dt><a name="index-GSL_005fSET_005fIMAG"></a>Macro: <strong>GSL_SET_IMAG</strong> <em>(<var>zp</var>,<var>y</var>)</em></dt>
<dd><p>These macros allow the real and imaginary parts of the complex number
pointed to by <var>zp</var> to be set independently.
</p></dd></dl>

<hr>
<div class="header">
<p>
Next: <a href="Properties-of-complex-numbers.html#Properties-of-complex-numbers" accesskey="n" rel="next">Properties of complex numbers</a>, Up: <a href="Complex-Numbers.html#Complex-Numbers" accesskey="u" rel="up">Complex Numbers</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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