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<li><a class="reference internal" href="#">Complex Number Objects</a><ul>
<li><a class="reference internal" href="#complex-numbers-as-c-structures">Complex Numbers as C Structures</a></li>
<li><a class="reference internal" href="#complex-numbers-as-python-objects">Complex Numbers as Python Objects</a></li>
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  <section id="complex-number-objects">
<span id="complexobjects"></span><h1>Complex Number Objects<a class="headerlink" href="#complex-number-objects" title="Link to this heading">¶</a></h1>
<p id="index-0">Python’s complex number objects are implemented as two distinct types when
viewed from the C API:  one is the Python object exposed to Python programs, and
the other is a C structure which represents the actual complex number value.
The API provides functions for working with both.</p>
<section id="complex-numbers-as-c-structures">
<h2>Complex Numbers as C Structures<a class="headerlink" href="#complex-numbers-as-c-structures" title="Link to this heading">¶</a></h2>
<p>Note that the functions which accept these structures as parameters and return
them as results do so <em>by value</em> rather than dereferencing them through
pointers.  This is consistent throughout the API.</p>
<dl class="c type">
<dt class="sig sig-object c" id="c.Py_complex">
<span class="k"><span class="pre">type</span></span><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">Py_complex</span></span></span><a class="headerlink" href="#c.Py_complex" title="Link to this definition">¶</a><br /></dt>
<dd><p>The C structure which corresponds to the value portion of a Python complex
number object.  Most of the functions for dealing with complex number objects
use structures of this type as input or output values, as appropriate.</p>
<dl class="c member">
<dt class="sig sig-object c" id="c.Py_complex.real">
<span class="kt"><span class="pre">double</span></span><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">real</span></span></span><a class="headerlink" href="#c.Py_complex.real" title="Link to this definition">¶</a><br /></dt>
<dt class="sig sig-object c" id="c.Py_complex.imag">
<span class="kt"><span class="pre">double</span></span><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">imag</span></span></span><a class="headerlink" href="#c.Py_complex.imag" title="Link to this definition">¶</a><br /></dt>
<dd></dd></dl>

<p>The structure is defined as:</p>
<div class="highlight-c notranslate"><div class="highlight"><pre><span></span><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="p">{</span>
<span class="w">    </span><span class="kt">double</span><span class="w"> </span><span class="n">real</span><span class="p">;</span>
<span class="w">    </span><span class="kt">double</span><span class="w"> </span><span class="n">imag</span><span class="p">;</span>
<span class="p">}</span><span class="w"> </span><span class="n">Py_complex</span><span class="p">;</span>
</pre></div>
</div>
</dd></dl>

<dl class="c function">
<dt class="sig sig-object c" id="c._Py_c_sum">
<a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">_Py_c_sum</span></span></span><span class="sig-paren">(</span><a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="n"><span class="pre">left</span></span>, <a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="n"><span class="pre">right</span></span><span class="sig-paren">)</span><a class="headerlink" href="#c._Py_c_sum" title="Link to this definition">¶</a><br /></dt>
<dd><p>Return the sum of two complex numbers, using the C <a class="reference internal" href="#c.Py_complex" title="Py_complex"><code class="xref c c-type docutils literal notranslate"><span class="pre">Py_complex</span></code></a>
representation.</p>
</dd></dl>

<dl class="c function">
<dt class="sig sig-object c" id="c._Py_c_diff">
<a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">_Py_c_diff</span></span></span><span class="sig-paren">(</span><a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="n"><span class="pre">left</span></span>, <a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="n"><span class="pre">right</span></span><span class="sig-paren">)</span><a class="headerlink" href="#c._Py_c_diff" title="Link to this definition">¶</a><br /></dt>
<dd><p>Return the difference between two complex numbers, using the C
<a class="reference internal" href="#c.Py_complex" title="Py_complex"><code class="xref c c-type docutils literal notranslate"><span class="pre">Py_complex</span></code></a> representation.</p>
</dd></dl>

<dl class="c function">
<dt class="sig sig-object c" id="c._Py_c_neg">
<a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">_Py_c_neg</span></span></span><span class="sig-paren">(</span><a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="n"><span class="pre">num</span></span><span class="sig-paren">)</span><a class="headerlink" href="#c._Py_c_neg" title="Link to this definition">¶</a><br /></dt>
<dd><p>Return the negation of the complex number <em>num</em>, using the C
<a class="reference internal" href="#c.Py_complex" title="Py_complex"><code class="xref c c-type docutils literal notranslate"><span class="pre">Py_complex</span></code></a> representation.</p>
</dd></dl>

<dl class="c function">
<dt class="sig sig-object c" id="c._Py_c_prod">
<a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">_Py_c_prod</span></span></span><span class="sig-paren">(</span><a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="n"><span class="pre">left</span></span>, <a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="n"><span class="pre">right</span></span><span class="sig-paren">)</span><a class="headerlink" href="#c._Py_c_prod" title="Link to this definition">¶</a><br /></dt>
<dd><p>Return the product of two complex numbers, using the C <a class="reference internal" href="#c.Py_complex" title="Py_complex"><code class="xref c c-type docutils literal notranslate"><span class="pre">Py_complex</span></code></a>
representation.</p>
</dd></dl>

<dl class="c function">
<dt class="sig sig-object c" id="c._Py_c_quot">
<a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">_Py_c_quot</span></span></span><span class="sig-paren">(</span><a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="n"><span class="pre">dividend</span></span>, <a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="n"><span class="pre">divisor</span></span><span class="sig-paren">)</span><a class="headerlink" href="#c._Py_c_quot" title="Link to this definition">¶</a><br /></dt>
<dd><p>Return the quotient of two complex numbers, using the C <a class="reference internal" href="#c.Py_complex" title="Py_complex"><code class="xref c c-type docutils literal notranslate"><span class="pre">Py_complex</span></code></a>
representation.</p>
<p>If <em>divisor</em> is null, this method returns zero and sets
<code class="xref c c-data docutils literal notranslate"><span class="pre">errno</span></code> to <code class="xref c c-macro docutils literal notranslate"><span class="pre">EDOM</span></code>.</p>
</dd></dl>

<dl class="c function">
<dt class="sig sig-object c" id="c._Py_c_pow">
<a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">_Py_c_pow</span></span></span><span class="sig-paren">(</span><a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="n"><span class="pre">num</span></span>, <a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="n"><span class="pre">exp</span></span><span class="sig-paren">)</span><a class="headerlink" href="#c._Py_c_pow" title="Link to this definition">¶</a><br /></dt>
<dd><p>Return the exponentiation of <em>num</em> by <em>exp</em>, using the C <a class="reference internal" href="#c.Py_complex" title="Py_complex"><code class="xref c c-type docutils literal notranslate"><span class="pre">Py_complex</span></code></a>
representation.</p>
<p>If <em>num</em> is null and <em>exp</em> is not a positive real number,
this method returns zero and sets <code class="xref c c-data docutils literal notranslate"><span class="pre">errno</span></code> to <code class="xref c c-macro docutils literal notranslate"><span class="pre">EDOM</span></code>.</p>
<p>Set <code class="xref c c-data docutils literal notranslate"><span class="pre">errno</span></code> to <code class="xref c c-macro docutils literal notranslate"><span class="pre">ERANGE</span></code> on overflows.</p>
</dd></dl>

</section>
<section id="complex-numbers-as-python-objects">
<h2>Complex Numbers as Python Objects<a class="headerlink" href="#complex-numbers-as-python-objects" title="Link to this heading">¶</a></h2>
<dl class="c type">
<dt class="sig sig-object c" id="c.PyComplexObject">
<span class="k"><span class="pre">type</span></span><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">PyComplexObject</span></span></span><a class="headerlink" href="#c.PyComplexObject" title="Link to this definition">¶</a><br /></dt>
<dd><p>This subtype of <a class="reference internal" href="structures.html#c.PyObject" title="PyObject"><code class="xref c c-type docutils literal notranslate"><span class="pre">PyObject</span></code></a> represents a Python complex number object.</p>
</dd></dl>

<dl class="c var">
<dt class="sig sig-object c" id="c.PyComplex_Type">
<a class="reference internal" href="type.html#c.PyTypeObject" title="PyTypeObject"><span class="n"><span class="pre">PyTypeObject</span></span></a><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">PyComplex_Type</span></span></span><a class="headerlink" href="#c.PyComplex_Type" title="Link to this definition">¶</a><br /></dt>
<dd><em class="stableabi"> Part of the <a class="reference internal" href="stable.html#stable"><span class="std std-ref">Stable ABI</span></a>.</em><p>This instance of <a class="reference internal" href="type.html#c.PyTypeObject" title="PyTypeObject"><code class="xref c c-type docutils literal notranslate"><span class="pre">PyTypeObject</span></code></a> represents the Python complex number
type. It is the same object as <a class="reference internal" href="../library/functions.html#complex" title="complex"><code class="xref py py-class docutils literal notranslate"><span class="pre">complex</span></code></a> in the Python layer.</p>
</dd></dl>

<dl class="c function">
<dt class="sig sig-object c" id="c.PyComplex_Check">
<span class="kt"><span class="pre">int</span></span><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">PyComplex_Check</span></span></span><span class="sig-paren">(</span><a class="reference internal" href="structures.html#c.PyObject" title="PyObject"><span class="n"><span class="pre">PyObject</span></span></a><span class="w"> </span><span class="p"><span class="pre">*</span></span><span class="n"><span class="pre">p</span></span><span class="sig-paren">)</span><a class="headerlink" href="#c.PyComplex_Check" title="Link to this definition">¶</a><br /></dt>
<dd><p>Return true if its argument is a <a class="reference internal" href="#c.PyComplexObject" title="PyComplexObject"><code class="xref c c-type docutils literal notranslate"><span class="pre">PyComplexObject</span></code></a> or a subtype of
<code class="xref c c-type docutils literal notranslate"><span class="pre">PyComplexObject</span></code>.  This function always succeeds.</p>
</dd></dl>

<dl class="c function">
<dt class="sig sig-object c" id="c.PyComplex_CheckExact">
<span class="kt"><span class="pre">int</span></span><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">PyComplex_CheckExact</span></span></span><span class="sig-paren">(</span><a class="reference internal" href="structures.html#c.PyObject" title="PyObject"><span class="n"><span class="pre">PyObject</span></span></a><span class="w"> </span><span class="p"><span class="pre">*</span></span><span class="n"><span class="pre">p</span></span><span class="sig-paren">)</span><a class="headerlink" href="#c.PyComplex_CheckExact" title="Link to this definition">¶</a><br /></dt>
<dd><p>Return true if its argument is a <a class="reference internal" href="#c.PyComplexObject" title="PyComplexObject"><code class="xref c c-type docutils literal notranslate"><span class="pre">PyComplexObject</span></code></a>, but not a subtype of
<code class="xref c c-type docutils literal notranslate"><span class="pre">PyComplexObject</span></code>.  This function always succeeds.</p>
</dd></dl>

<dl class="c function">
<dt class="sig sig-object c" id="c.PyComplex_FromCComplex">
<a class="reference internal" href="structures.html#c.PyObject" title="PyObject"><span class="n"><span class="pre">PyObject</span></span></a><span class="w"> </span><span class="p"><span class="pre">*</span></span><span class="sig-name descname"><span class="n"><span class="pre">PyComplex_FromCComplex</span></span></span><span class="sig-paren">(</span><a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="n"><span class="pre">v</span></span><span class="sig-paren">)</span><a class="headerlink" href="#c.PyComplex_FromCComplex" title="Link to this definition">¶</a><br /></dt>
<dd><em class="refcount return_new_ref">Return value: New reference.</em><p>Create a new Python complex number object from a C <a class="reference internal" href="#c.Py_complex" title="Py_complex"><code class="xref c c-type docutils literal notranslate"><span class="pre">Py_complex</span></code></a> value.
Return <code class="docutils literal notranslate"><span class="pre">NULL</span></code> with an exception set on error.</p>
</dd></dl>

<dl class="c function">
<dt class="sig sig-object c" id="c.PyComplex_FromDoubles">
<a class="reference internal" href="structures.html#c.PyObject" title="PyObject"><span class="n"><span class="pre">PyObject</span></span></a><span class="w"> </span><span class="p"><span class="pre">*</span></span><span class="sig-name descname"><span class="n"><span class="pre">PyComplex_FromDoubles</span></span></span><span class="sig-paren">(</span><span class="kt"><span class="pre">double</span></span><span class="w"> </span><span class="n"><span class="pre">real</span></span>, <span class="kt"><span class="pre">double</span></span><span class="w"> </span><span class="n"><span class="pre">imag</span></span><span class="sig-paren">)</span><a class="headerlink" href="#c.PyComplex_FromDoubles" title="Link to this definition">¶</a><br /></dt>
<dd><em class="refcount return_new_ref">Return value: New reference.</em><em class="stableabi"> Part of the <a class="reference internal" href="stable.html#stable"><span class="std std-ref">Stable ABI</span></a>.</em><p>Return a new <a class="reference internal" href="#c.PyComplexObject" title="PyComplexObject"><code class="xref c c-type docutils literal notranslate"><span class="pre">PyComplexObject</span></code></a> object from <em>real</em> and <em>imag</em>.
Return <code class="docutils literal notranslate"><span class="pre">NULL</span></code> with an exception set on error.</p>
</dd></dl>

<dl class="c function">
<dt class="sig sig-object c" id="c.PyComplex_RealAsDouble">
<span class="kt"><span class="pre">double</span></span><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">PyComplex_RealAsDouble</span></span></span><span class="sig-paren">(</span><a class="reference internal" href="structures.html#c.PyObject" title="PyObject"><span class="n"><span class="pre">PyObject</span></span></a><span class="w"> </span><span class="p"><span class="pre">*</span></span><span class="n"><span class="pre">op</span></span><span class="sig-paren">)</span><a class="headerlink" href="#c.PyComplex_RealAsDouble" title="Link to this definition">¶</a><br /></dt>
<dd><em class="stableabi"> Part of the <a class="reference internal" href="stable.html#stable"><span class="std std-ref">Stable ABI</span></a>.</em><p>Return the real part of <em>op</em> as a C <span class="c-expr sig sig-inline c"><span class="kt">double</span></span>.</p>
<p>If <em>op</em> is not a Python complex number object but has a
<a class="reference internal" href="../reference/datamodel.html#object.__complex__" title="object.__complex__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__complex__()</span></code></a> method, this method will first be called to
convert <em>op</em> to a Python complex number object.  If <code class="xref py py-meth docutils literal notranslate"><span class="pre">__complex__()</span></code> is
not defined then it falls back to call <a class="reference internal" href="float.html#c.PyFloat_AsDouble" title="PyFloat_AsDouble"><code class="xref c c-func docutils literal notranslate"><span class="pre">PyFloat_AsDouble()</span></code></a> and
returns its result.</p>
<p>Upon failure, this method returns <code class="docutils literal notranslate"><span class="pre">-1.0</span></code> with an exception set, so one
should call <a class="reference internal" href="exceptions.html#c.PyErr_Occurred" title="PyErr_Occurred"><code class="xref c c-func docutils literal notranslate"><span class="pre">PyErr_Occurred()</span></code></a> to check for errors.</p>
<div class="versionchanged">
<p><span class="versionmodified changed">Changed in version 3.13: </span>Use <a class="reference internal" href="../reference/datamodel.html#object.__complex__" title="object.__complex__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__complex__()</span></code></a> if available.</p>
</div>
</dd></dl>

<dl class="c function">
<dt class="sig sig-object c" id="c.PyComplex_ImagAsDouble">
<span class="kt"><span class="pre">double</span></span><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">PyComplex_ImagAsDouble</span></span></span><span class="sig-paren">(</span><a class="reference internal" href="structures.html#c.PyObject" title="PyObject"><span class="n"><span class="pre">PyObject</span></span></a><span class="w"> </span><span class="p"><span class="pre">*</span></span><span class="n"><span class="pre">op</span></span><span class="sig-paren">)</span><a class="headerlink" href="#c.PyComplex_ImagAsDouble" title="Link to this definition">¶</a><br /></dt>
<dd><em class="stableabi"> Part of the <a class="reference internal" href="stable.html#stable"><span class="std std-ref">Stable ABI</span></a>.</em><p>Return the imaginary part of <em>op</em> as a C <span class="c-expr sig sig-inline c"><span class="kt">double</span></span>.</p>
<p>If <em>op</em> is not a Python complex number object but has a
<a class="reference internal" href="../reference/datamodel.html#object.__complex__" title="object.__complex__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__complex__()</span></code></a> method, this method will first be called to
convert <em>op</em> to a Python complex number object.  If <code class="xref py py-meth docutils literal notranslate"><span class="pre">__complex__()</span></code> is
not defined then it falls back to call <a class="reference internal" href="float.html#c.PyFloat_AsDouble" title="PyFloat_AsDouble"><code class="xref c c-func docutils literal notranslate"><span class="pre">PyFloat_AsDouble()</span></code></a> and
returns <code class="docutils literal notranslate"><span class="pre">0.0</span></code> on success.</p>
<p>Upon failure, this method returns <code class="docutils literal notranslate"><span class="pre">-1.0</span></code> with an exception set, so one
should call <a class="reference internal" href="exceptions.html#c.PyErr_Occurred" title="PyErr_Occurred"><code class="xref c c-func docutils literal notranslate"><span class="pre">PyErr_Occurred()</span></code></a> to check for errors.</p>
<div class="versionchanged">
<p><span class="versionmodified changed">Changed in version 3.13: </span>Use <a class="reference internal" href="../reference/datamodel.html#object.__complex__" title="object.__complex__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__complex__()</span></code></a> if available.</p>
</div>
</dd></dl>

<dl class="c function">
<dt class="sig sig-object c" id="c.PyComplex_AsCComplex">
<a class="reference internal" href="#c.Py_complex" title="Py_complex"><span class="n"><span class="pre">Py_complex</span></span></a><span class="w"> </span><span class="sig-name descname"><span class="n"><span class="pre">PyComplex_AsCComplex</span></span></span><span class="sig-paren">(</span><a class="reference internal" href="structures.html#c.PyObject" title="PyObject"><span class="n"><span class="pre">PyObject</span></span></a><span class="w"> </span><span class="p"><span class="pre">*</span></span><span class="n"><span class="pre">op</span></span><span class="sig-paren">)</span><a class="headerlink" href="#c.PyComplex_AsCComplex" title="Link to this definition">¶</a><br /></dt>
<dd><p>Return the <a class="reference internal" href="#c.Py_complex" title="Py_complex"><code class="xref c c-type docutils literal notranslate"><span class="pre">Py_complex</span></code></a> value of the complex number <em>op</em>.</p>
<p>If <em>op</em> is not a Python complex number object but has a <a class="reference internal" href="../reference/datamodel.html#object.__complex__" title="object.__complex__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__complex__()</span></code></a>
method, this method will first be called to convert <em>op</em> to a Python complex
number object.  If <code class="xref py py-meth docutils literal notranslate"><span class="pre">__complex__()</span></code> is not defined then it falls back to
<a class="reference internal" href="../reference/datamodel.html#object.__float__" title="object.__float__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__float__()</span></code></a>.  If <code class="xref py py-meth docutils literal notranslate"><span class="pre">__float__()</span></code> is not defined then it falls back
to <a class="reference internal" href="../reference/datamodel.html#object.__index__" title="object.__index__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__index__()</span></code></a>.</p>
<p>Upon failure, this method returns <a class="reference internal" href="#c.Py_complex" title="Py_complex"><code class="xref c c-type docutils literal notranslate"><span class="pre">Py_complex</span></code></a>
with <a class="reference internal" href="#c.Py_complex.real" title="Py_complex.real"><code class="xref c c-member docutils literal notranslate"><span class="pre">real</span></code></a> set to <code class="docutils literal notranslate"><span class="pre">-1.0</span></code> and with an exception set, so one
should call <a class="reference internal" href="exceptions.html#c.PyErr_Occurred" title="PyErr_Occurred"><code class="xref c c-func docutils literal notranslate"><span class="pre">PyErr_Occurred()</span></code></a> to check for errors.</p>
<div class="versionchanged">
<p><span class="versionmodified changed">Changed in version 3.8: </span>Use <a class="reference internal" href="../reference/datamodel.html#object.__index__" title="object.__index__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__index__()</span></code></a> if available.</p>
</div>
</dd></dl>

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<li><a class="reference internal" href="#">Complex Number Objects</a><ul>
<li><a class="reference internal" href="#complex-numbers-as-c-structures">Complex Numbers as C Structures</a></li>
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