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<header data-kunai-mdinfo="{"meta": {"header": ["complex"], "namespace": ["std"], "id-type": ["class template"]}, "sources": [{"id": "3ff32c2b7b9c33d0a8532f9cbe7fc2d1c8e3aeb5", "source": "#include <iostream>\n#include <complex>\n\nfloat pi()\n{\n return 3.141593f;\n}\n\nint main()\n{\n // \u5b9f\u90e81.0f\u3001\u865a\u90e82.0f\u306e\u8907\u7d20\u6570\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3092\u4f5c\u308b\n std::complex<float> c(1.0f, 2.0f);\n\n // \u30b9\u30c8\u30ea\u30fc\u30e0\u51fa\u529b\n std::cout << \"output : \" << c << std::endl;\n\n // \u5404\u8981\u7d20\u306e\u53d6\u5f97\n float real = c.real(); // \u5b9f\u90e8\n float imag = c.imag(); // \u865a\u90e8\n std::cout << \"real : \" << real << std::endl;\n std::cout << \"imag : \" << imag << std::endl;\n\n // \u6f14\u7b97\n std::complex<float> a(1.0f, 2.0f);\n std::complex<float> b(2.0f, 3.0f);\n std::cout << \"a + b : \" << a + b << std::endl;\n std::cout << \"a - b : \" << a - b << std::endl;\n std::cout << \"a * b : \" << a * b << std::endl;\n std::cout << \"a / b : \" << a / b << std::endl;\n\n // \u5404\u8907\u7d20\u6570\u306e\u5024\u3092\u53d6\u5f97\u3059\u308b\n std::cout << \"abs : \" << std::abs(c) << std::endl; // \u7d76\u5bfe\u5024\n std::cout << \"arg : \" << std::arg(c) << std::endl; // \u504f\u89d2\n std::cout << \"norm : \" << std::norm(c) << std::endl; // \u30ce\u30eb\u30e0\n std::cout << \"conj : \" << std::conj(c) << std::endl; // \u5171\u5f79\u8907\u7d20\u6570\n std::cout << \"proj : \" << std::proj(c) << std::endl; // \u30ea\u30fc\u30de\u30f3\u7403\u9762\u3078\u306e\u5c04\u5f71\n std::cout << \"polar : \" << std::polar(1.0f, pi() / 2.0f); // \u6975\u5ea7\u6a19(\u7d76\u5bfe\u5024\uff1a1.0\u3001\u504f\u89d2\uff1a\u5186\u5468\u7387\u00f72.0)\u304b\u3089\u8907\u7d20\u6570\u3092\u4f5c\u308b\n}\n"}, {"id": "3ef18b2de5013754c308d830ec02bede9f3b4cff", "source": "#include <print>\n#include <complex>\n#include <vector>\n#include <ranges>\n\nint main()\n{\n // \u69cb\u9020\u5316\u675f\u7e1b\u3067\u5404\u8981\u7d20\u3092\u53d6\u5f97\u3059\u308b\n {\n std::complex<float> c{1.0f, 2.0f};\n auto [real, imag] = c;\n std::println(\"real:{} imag:{}\", real, imag);\n }\n\n // \u5b9a\u6570\u306e\u6dfb\u5b57\u3092\u6307\u5b9a\u3057\u3066\u5404\u8981\u7d20\u3092\u53d6\u5f97\u3059\u308b\n {\n std::complex<float> c{1.0f, 2.0f};\n float real = std::get<0>(c);\n float imag = std::get<1>(c);\n std::println(\"real:{} imag:{}\", real, imag);\n }\n\n // complex\u306e\u914d\u5217\u304b\u3089\u5b9f\u90e8\u306e\u307f\u3092\u62bd\u51fa\u3059\u308b\n {\n std::vector<std::complex<float>> v {\n {1.0f, 2.0f},\n {3.0f, 4.0f},\n {5.0f, 6.0f}\n };\n\n for (float real : v | std::views::elements<0>) {\n std::println(\"real:{}\", real);\n }\n }\n}\n"}], "page_id": ["reference", "complex", "complex"]}">
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<div class="identifier-type">class template</div><div class="header"><complex></div><h1 itemprop="name"><span class="namespace" title="namespace std">std::</span><span class="token">complex</span></h1>
<div itemprop="articleBody"><p><div class="codehilite"><pre><span></span><code><span class="k">namespace</span><span class="w"> </span><span class="nn">std</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="k">template</span><span class="w"> </span><span class="o"><</span><span class="k">class</span><span class="w"> </span><span class="nc">T</span><span class="o">></span>
<span class="w"> </span><span class="k">class</span><span class="w"> </span><span class="nc">complex</span><span class="p">;</span>
<span class="p">}</span>
</code></pre></div>
</p>
<p><code><complex></code>ヘッダでは、複素数を扱うクラスおよび関数を定義する。</p>
<p><code>complex</code>クラステンプレートは、複素数を表すクラスである。このクラスは、実部(real part)と虚部(imaginary part)を、それぞれ型<code>T</code>の値として保持し、演算に使用する。</p>
<p><code>complex</code>クラステンプレートは<a class="cpprefjp-defined-word" data-desc="型をconstおよび・もしくはvolatileで修飾すること">CV修飾</a>されていない浮動小数点数型 (C++23以降は<a class="cpprefjp-defined-word" data-desc="<stdfloat>で定義される内部表現の規定された浮動小数点数型" href="../stdfloat.html">拡張浮動小数点数型</a>を含む) で特殊化され、特化した実装が行われる：</p>
<p>これ以外の型がテンプレート引数として与えられた場合、その動作は<a class="cpprefjp-defined-word" data-desc="未規定の動作。事前の断りなく処理系によって異なる動作をする" href="../../implementation-compliance.html#dfn-unspecified-behavior">未規定</a>である。</p>
<h3>配列へのキャスト(C++11)</h3>
<p><code>complex</code>クラスの左辺値オブジェクト<code>c</code>は、<code>reinterpret_cast<cv修飾 T(&)[2]>(c)</code>もしくは<code>reinterpret_cast<cv修飾 T*>(&c)</code>で浮動小数点数型の配列にキャスト可能である。その場合、配列の<code>0</code>番目は実部を表し、<code>1</code>番目は虚部を表す。</p>
<h2>メンバ関数</h2>
<table border="1" bordercolor="#888" style="border-collapse:collapse">
<thead>
<tr>
<th>名前</th>
<th>説明</th>
<th>対応バージョン</th>
</tr>
</thead>
<tbody>
<tr>
<td><code><a href="complex/op_constructor.html">(constructor)</a></code></td>
<td>コンストラクタ</td>
<td></td>
</tr>
<tr>
<td><code>~complex() = default;</code></td>
<td>デストラクタ</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/real.html">real</a></code></td>
<td>複素数値の実部を取得／設定する</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/imag.html">imag</a></code></td>
<td>複素数値の虚部を取得／設定する</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/op_assign.html">operator=</a></code></td>
<td>複素数値のコピー</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/op_plus_assign.html">operator+=</a></code></td>
<td>複素数値の加算</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/op_minus_assign.html">operator-=</a></code></td>
<td>複素数値の減算</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/op_multiply_assign.html">operator*=</a></code></td>
<td>複素数値の乗算</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/op_divide_assign.html">operator/=</a></code></td>
<td>複素数値の除算</td>
<td></td>
</tr>
</tbody>
</table>
<h2>メンバ型</h2>
<table border="1" bordercolor="#888" style="border-collapse:collapse">
<thead>
<tr>
<th>名前</th>
<th>説明</th>
<th>対応バージョン</th>
</tr>
</thead>
<tbody>
<tr>
<td><code>value_type</code></td>
<td>実部と虚部およびそれらの演算に使用する浮動小数点数型。テンプレートパラメータの型<code>T</code>。</td>
<td></td>
</tr>
</tbody>
</table>
<h2>非メンバ関数</h2>
<h3>複素数の値</h3>
<table border="1" bordercolor="#888" style="border-collapse:collapse">
<thead>
<tr>
<th>名前</th>
<th>説明</th>
<th>対応バージョン</th>
</tr>
</thead>
<tbody>
<tr>
<td><code><a href="complex/real_free.html">real</a></code></td>
<td>実部を取得する</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/imag_free.html">imag</a></code></td>
<td>虚部を取得する</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/abs.html">abs</a></code></td>
<td>複素数の絶対値を得る</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/arg.html">arg</a></code></td>
<td>複素数の偏角を得る</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/norm.html">norm</a></code></td>
<td>複素数体のノルムを得る</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/conj.html">conj</a></code></td>
<td>共役複素数を得る</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/proj.html">proj</a></code></td>
<td>リーマン球面への射影を得る</td>
<td>C++11</td>
</tr>
<tr>
<td><code><a href="complex/polar.html">polar</a></code></td>
<td>複素数を極形式で指定して作る</td>
<td></td>
</tr>
</tbody>
</table>
<h3>演算子</h3>
<table border="1" bordercolor="#888" style="border-collapse:collapse">
<thead>
<tr>
<th>名前</th>
<th>説明</th>
<th>対応バージョン</th>
</tr>
</thead>
<tbody>
<tr>
<td><a href="complex/op_unary_plus.html"><code>operator+</code> (単項)</a></td>
<td>単項 <code>+</code> 演算（引数をそのまま返す）</td>
<td></td>
</tr>
<tr>
<td><a href="complex/op_unary_minus.html"><code>operator-</code> (単項)</a></td>
<td>単項 <code>-</code> 演算（符号を反転した複素数値を得る）</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/op_plus.html">operator+</a></code></td>
<td><code>complex</code> オブジェクトを加算する</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/op_minus.html">operator-</a></code></td>
<td><code>complex</code> オブジェクトを減算する</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/op_multiply.html">operator*</a></code></td>
<td><code>complex</code> オブジェクトを乗算する</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/op_divide.html">operator/</a></code></td>
<td><code>complex</code> オブジェクトを除算する</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/op_equal.html">operator==</a></code></td>
<td><code>complex</code> オブジェクトを等値比較する</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/op_not_equal.html">operator!=</a></code></td>
<td><code>complex</code> オブジェクトを非等値比較する</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/op_ostream.html">operator<<</a></code></td>
<td>ストリームへの出力</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/op_istream.html">operator>></a></code></td>
<td>ストリームからの入力</td>
<td></td>
</tr>
</tbody>
</table>
<h3>リテラル</h3>
<table border="1" bordercolor="#888" style="border-collapse:collapse">
<thead>
<tr>
<th>名前</th>
<th>説明</th>
<th>対応バージョン</th>
</tr>
</thead>
<tbody>
<tr>
<td><code><a href="complex/op_i.html">i</a></code></td>
<td><code>complex<double></code>のリテラル</td>
<td>C++14</td>
</tr>
<tr>
<td><code><a href="complex/op_if.html">if</a></code></td>
<td><code>complex<float></code>のリテラル</td>
<td>C++14</td>
</tr>
<tr>
<td><code><a href="complex/op_il.html">il</a></code></td>
<td><code>complex<long double></code>のリテラル</td>
<td>C++14</td>
</tr>
</tbody>
</table>
<h3>数学関数の<code>complex</code>に対する<a class="cpprefjp-defined-word" data-desc="同名の関数を異なる引数・テンプレート・制約などで複数定義すること。または同名の関数の集合">オーバーロード</a></h3>
<table border="1" bordercolor="#888" style="border-collapse:collapse">
<thead>
<tr>
<th>名前</th>
<th>説明</th>
<th>対応バージョン</th>
</tr>
</thead>
<tbody>
<tr>
<td><code><a href="complex/acos.html">acos</a></code></td>
<td>複素数の逆余弦を求める</td>
<td>C++11</td>
</tr>
<tr>
<td><code><a href="complex/asin.html">asin</a></code></td>
<td>複素数の逆正弦を求める</td>
<td>C++11</td>
</tr>
<tr>
<td><code><a href="complex/atan.html">atan</a></code></td>
<td>複素数の逆正接を求める</td>
<td>C++11</td>
</tr>
<tr>
<td><code><a href="complex/acosh.html">acosh</a></code></td>
<td>複素数の双曲線逆余弦を求める</td>
<td>C++11</td>
</tr>
<tr>
<td><code><a href="complex/asinh.html">asinh</a></code></td>
<td>複素数の双曲線逆正弦を求める</td>
<td>C++11</td>
</tr>
<tr>
<td><code><a href="complex/atanh.html">atanh</a></code></td>
<td>複素数の双曲線逆正接を求める</td>
<td>C++11</td>
</tr>
<tr>
<td><code><a href="complex/cos.html">cos</a></code></td>
<td>複素数の余弦を求める</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/cosh.html">cosh</a></code></td>
<td>複素数の双曲線余弦を求める</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/exp.html">exp</a></code></td>
<td>自然対数の底 e の累乗（複素数）を求める。</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/log.html">log</a></code></td>
<td>複素数の自然対数を求める</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/log10.html">log10</a></code></td>
<td>複素数の常用対数を求める</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/pow.html">pow</a></code></td>
<td>複素数の累乗を求める</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/sin.html">sin</a></code></td>
<td>複素数の正弦を求める</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/sinh.html">sinh</a></code></td>
<td>複素数の双曲線正弦を求める</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/sqrt.html">sqrt</a></code></td>
<td>複素数の平方根を求める</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/tan.html">tan</a></code></td>
<td>複素数の正接を求める</td>
<td></td>
</tr>
<tr>
<td><code><a href="complex/tanh.html">tanh</a></code></td>
<td>複素数の双曲線正接を求める</td>
<td></td>
</tr>
</tbody>
</table>
<h2>タプルインタフェースサポート</h2>
<table border="1" bordercolor="#888" style="border-collapse:collapse">
<thead>
<tr>
<th>名前</th>
<th>説明</th>
<th>対応バージョン</th>
</tr>
</thead>
<tbody>
<tr>
<td><code><a href="complex/tuple_size.html">tuple_size</a></code></td>
<td>静的な要素数取得(class template)</td>
<td>C++26</td>
</tr>
<tr>
<td><code><a href="complex/tuple_element.html">tuple_element</a></code></td>
<td>静的な要素の型取得(class template)</td>
<td>C++26</td>
</tr>
<tr>
<td><code><a href="complex/get.html">get</a></code></td>
<td>要素を取得する(function template)</td>
<td>C++26</td>
</tr>
</tbody>
</table>
<h2>例</h2>
<h3>基本的な使い方</h3>
<p><div class="yata" id="3ff32c2b7b9c33d0a8532f9cbe7fc2d1c8e3aeb5"><div class="codehilite"><pre><span></span><code><span class="cp">#include <a href="../iostream.html"><iostream></a></span>
<span class="cp">#include <a href="../complex.html"><complex></a></span>
<span class="kt">float</span><span class="w"> </span><span class="nf">pi</span><span class="p">()</span>
<span class="p">{</span>
<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">3.141593f</span><span class="p">;</span>
<span class="p">}</span>
<span class="kt">int</span><span class="w"> </span><span class="nf">main</span><span class="p">()</span>
<span class="p">{</span>
<span class="w"> </span><span class="c1">// 実部1.0f、虚部2.0fの複素数オブジェクトを作る</span>
<span class="w"> </span><span class="n"><span style="color:#ff0000">std::complex</span></span><span class="o"><</span><span class="kt">float</span><span class="o">></span><span class="w"> </span><span class="n">c</span><span class="p">(</span><span class="mf">1.0f</span><span class="p">,</span><span class="w"> </span><span class="mf">2.0f</span><span class="p">);</span>
<span class="w"> </span><span class="c1">// ストリーム出力</span>
<span class="w"> </span><span class="n"><a href="../iostream/cout.html">std::cout</a></span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"output : "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="../ostream/endl.html">std::endl</a></span><span class="p">;</span>
<span class="w"> </span><span class="c1">// 各要素の取得</span>
<span class="w"> </span><span class="kt">float</span><span class="w"> </span><span class="n">real</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n"><a href="complex/real.html">c.real()</a></span><span class="p">;</span><span class="w"> </span><span class="c1">// 実部</span>
<span class="w"> </span><span class="kt">float</span><span class="w"> </span><span class="n">imag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n"><a href="complex/imag.html">c.imag()</a></span><span class="p">;</span><span class="w"> </span><span class="c1">// 虚部</span>
<span class="w"> </span><span class="n"><a href="../iostream/cout.html">std::cout</a></span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"real : "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">real</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="../ostream/endl.html">std::endl</a></span><span class="p">;</span>
<span class="w"> </span><span class="n"><a href="../iostream/cout.html">std::cout</a></span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"imag : "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">imag</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="../ostream/endl.html">std::endl</a></span><span class="p">;</span>
<span class="w"> </span><span class="c1">// 演算</span>
<span class="w"> </span><span class="n"><span style="color:#ff0000">std::complex</span></span><span class="o"><</span><span class="kt">float</span><span class="o">></span><span class="w"> </span><span class="n">a</span><span class="p">(</span><span class="mf">1.0f</span><span class="p">,</span><span class="w"> </span><span class="mf">2.0f</span><span class="p">);</span>
<span class="w"> </span><span class="n"><span style="color:#ff0000">std::complex</span></span><span class="o"><</span><span class="kt">float</span><span class="o">></span><span class="w"> </span><span class="n">b</span><span class="p">(</span><span class="mf">2.0f</span><span class="p">,</span><span class="w"> </span><span class="mf">3.0f</span><span class="p">);</span>
<span class="w"> </span><span class="n"><a href="../iostream/cout.html">std::cout</a></span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"a + b : "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="../ostream/endl.html">std::endl</a></span><span class="p">;</span>
<span class="w"> </span><span class="n"><a href="../iostream/cout.html">std::cout</a></span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"a - b : "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="../ostream/endl.html">std::endl</a></span><span class="p">;</span>
<span class="w"> </span><span class="n"><a href="../iostream/cout.html">std::cout</a></span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"a * b : "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="../ostream/endl.html">std::endl</a></span><span class="p">;</span>
<span class="w"> </span><span class="n"><a href="../iostream/cout.html">std::cout</a></span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"a / b : "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="../ostream/endl.html">std::endl</a></span><span class="p">;</span>
<span class="w"> </span><span class="c1">// 各複素数の値を取得する</span>
<span class="w"> </span><span class="n"><a href="../iostream/cout.html">std::cout</a></span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"abs : "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="complex/abs.html">std::abs</a></span><span class="p">(</span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="../ostream/endl.html">std::endl</a></span><span class="p">;</span><span class="w"> </span><span class="c1">// 絶対値</span>
<span class="w"> </span><span class="n"><a href="../iostream/cout.html">std::cout</a></span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"arg : "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="complex/arg.html">std::arg</a></span><span class="p">(</span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="../ostream/endl.html">std::endl</a></span><span class="p">;</span><span class="w"> </span><span class="c1">// 偏角</span>
<span class="w"> </span><span class="n"><a href="../iostream/cout.html">std::cout</a></span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"norm : "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="complex/norm.html">std::norm</a></span><span class="p">(</span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="../ostream/endl.html">std::endl</a></span><span class="p">;</span><span class="w"> </span><span class="c1">// ノルム</span>
<span class="w"> </span><span class="n"><a href="../iostream/cout.html">std::cout</a></span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"conj : "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="complex/conj.html">std::conj</a></span><span class="p">(</span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="../ostream/endl.html">std::endl</a></span><span class="p">;</span><span class="w"> </span><span class="c1">// 共役複素数</span>
<span class="w"> </span><span class="n"><a href="../iostream/cout.html">std::cout</a></span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"proj : "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="complex/proj.html">std::proj</a></span><span class="p">(</span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="../ostream/endl.html">std::endl</a></span><span class="p">;</span><span class="w"> </span><span class="c1">// リーマン球面への射影</span>
<span class="w"> </span><span class="n"><a href="../iostream/cout.html">std::cout</a></span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"polar : "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="complex/polar.html">std::polar</a></span><span class="p">(</span><span class="mf">1.0f</span><span class="p">,</span><span class="w"> </span><span class="n">pi</span><span class="p">()</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2.0f</span><span class="p">);</span><span class="w"> </span><span class="c1">// 極座標(絶対値：1.0、偏角：円周率÷2.0)から複素数を作る</span>
<span class="p">}</span>
</code></pre></div>
</div></p>
<h4>出力</h4>
<p><pre><code>output : (1,2)
real : 1
imag : 2
a + b : (3,5)
a - b : (-1,-1)
a * b : (-4,7)
a / b : (0.615385,0.0769231)
abs : 2.23607
arg : 1.10715
norm : 5
conj : (1,-2)
proj : (1,2)
polar : (-1.62921e-07,1)
</code></pre></p>
<h3>タプルインタフェースを使用する (C++26)</h3>
<p><div class="yata" id="3ef18b2de5013754c308d830ec02bede9f3b4cff"><div class="codehilite"><pre><span></span><code><span class="cp">#include <a href="../print.html"><print></a></span>
<span class="cp">#include <a href="../complex.html"><complex></a></span>
<span class="cp">#include <a href="../vector.html"><vector></a></span>
<span class="cp">#include <a href="../ranges.html"><ranges></a></span>
<span class="kt">int</span><span class="w"> </span><span class="nf">main</span><span class="p">()</span>
<span class="p">{</span>
<span class="w"> </span><span class="c1">// 構造化束縛で各要素を取得する</span>
<span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">complex</span><span class="o"><</span><span class="kt">float</span><span class="o">></span><span class="w"> </span><span class="n">c</span><span class="p">{</span><span class="mf">1.0f</span><span class="p">,</span><span class="w"> </span><span class="mf">2.0f</span><span class="p">};</span>
<span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="p">[</span><span class="n">real</span><span class="p">,</span><span class="w"> </span><span class="n">imag</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">c</span><span class="p">;</span>
<span class="w"> </span><span class="n"><a href="../print/println.html">std::println</a></span><span class="p">(</span><span class="s">"real:{} imag:{}"</span><span class="p">,</span><span class="w"> </span><span class="n">real</span><span class="p">,</span><span class="w"> </span><span class="n">imag</span><span class="p">);</span>
<span class="w"> </span><span class="p">}</span>
<span class="w"> </span><span class="c1">// 定数の添字を指定して各要素を取得する</span>
<span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">complex</span><span class="o"><</span><span class="kt">float</span><span class="o">></span><span class="w"> </span><span class="n">c</span><span class="p">{</span><span class="mf">1.0f</span><span class="p">,</span><span class="w"> </span><span class="mf">2.0f</span><span class="p">};</span>
<span class="w"> </span><span class="kt">float</span><span class="w"> </span><span class="n">real</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n"><a href="complex/get.html">std::get</a></span><span class="o"><</span><span class="mi">0</span><span class="o">></span><span class="p">(</span><span class="n">c</span><span class="p">);</span>
<span class="w"> </span><span class="kt">float</span><span class="w"> </span><span class="n">imag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n"><a href="complex/get.html">std::get</a></span><span class="o"><</span><span class="mi">1</span><span class="o">></span><span class="p">(</span><span class="n">c</span><span class="p">);</span>
<span class="w"> </span><span class="n"><a href="../print/println.html">std::println</a></span><span class="p">(</span><span class="s">"real:{} imag:{}"</span><span class="p">,</span><span class="w"> </span><span class="n">real</span><span class="p">,</span><span class="w"> </span><span class="n">imag</span><span class="p">);</span>
<span class="w"> </span><span class="p">}</span>
<span class="w"> </span><span class="c1">// complexの配列から実部のみを抽出する</span>
<span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="n"><a href="../vector/vector.html">std::vector</a></span><span class="o"><</span><span class="n">std</span><span class="o">::</span><span class="n">complex</span><span class="o"><</span><span class="kt">float</span><span class="o">>></span><span class="w"> </span><span class="n">v</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="p">{</span><span class="mf">1.0f</span><span class="p">,</span><span class="w"> </span><span class="mf">2.0f</span><span class="p">},</span>
<span class="w"> </span><span class="p">{</span><span class="mf">3.0f</span><span class="p">,</span><span class="w"> </span><span class="mf">4.0f</span><span class="p">},</span>
<span class="w"> </span><span class="p">{</span><span class="mf">5.0f</span><span class="p">,</span><span class="w"> </span><span class="mf">6.0f</span><span class="p">}</span>
<span class="w"> </span><span class="p">};</span>
<span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">real</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">v</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="n"><a href="../ranges/elements_view.html">std::views::elements</a></span><span class="o"><</span><span class="mi">0</span><span class="o">></span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="n"><a href="../print/println.html">std::println</a></span><span class="p">(</span><span class="s">"real:{}"</span><span class="p">,</span><span class="w"> </span><span class="n">real</span><span class="p">);</span>
<span class="w"> </span><span class="p">}</span>
<span class="w"> </span><span class="p">}</span>
<span class="p">}</span>
</code></pre></div>
</div></p>
<h4>出力</h4>
<p><pre><code>real:1 imag:2
real:1 imag:2
real:1
real:3
real:5
</code></pre></p>
<h2>参照</h2>
<ul>
<li><a href="https://ja.wikipedia.org/wiki/複素数" target="_blank">複素数 - Wikipedia</a></li>
<li><a href="http://www.jeea.or.jp/course/contents/01109/" target="_blank">複素数の手ほどき - 日本電気技術者協会</a></li>
<li><a href="http://eman-physics.net/math/imaginary01.html" target="_blank">複素数とは何か - EMANの物理学</a></li>
<li><a href="http://www.open-std.org/jtc1/sc22/wg21/docs/lwg-defects.html#387" target="_blank">LWG Issue 387. <code>std::complex</code> over-encapsulated</a><ul>
<li>C++11で、<code>std::complex</code>型のメモリレイアウトが規定された経緯のレポート</li>
</ul>
</li>
<li><a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2004/n1568.htm" target="_blank">N1568 Proposed additions to TR-1 to improve compatibility with C99</a></li>
<li><a href="https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2022/p1467r9.html" target="_blank">P1467R9 Extended floating-point types and standard names</a><ul>
<li>C++23で<a class="cpprefjp-defined-word" data-desc="<stdfloat>で定義される内部表現の規定された浮動小数点数型" href="../stdfloat.html">拡張浮動小数点数型</a>に対応した</li>
</ul>
</li>
<li><a href="https://open-std.org/jtc1/sc22/wg21/docs/papers/2023/p2819r2.pdf" target="_blank">P2819R2 Add tuple protocol to complex</a><ul>
<li>C++26から<code>std::complex</code>にタプルインタフェースがサポートされた</li>
</ul>
</li>
</ul></div>
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