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| <h3 class="section">20.10 Projections, Conjugates, and Decomposing of Complex Numbers</h3> |
| |
| <p><a name="index-project-complex-numbers-2525"></a><a name="index-conjugate-complex-numbers-2526"></a><a name="index-decompose-complex-numbers-2527"></a><a name="index-complex_002eh-2528"></a> |
| ISO C99<!-- /@w --> also defines functions that perform basic operations on |
| complex numbers, such as decomposition and conjugation. The prototypes |
| for all these functions are in <samp><span class="file">complex.h</span></samp>. All functions are |
| available in three variants, one for each of the three complex types. |
| |
| <!-- complex.h --> |
| <!-- ISO --> |
| <div class="defun"> |
| — Function: double <b>creal</b> (<var>complex double z</var>)<var><a name="index-creal-2529"></a></var><br> |
| <blockquote><!-- complex.h --> |
| <!-- ISO --> |
| — Function: float <b>crealf</b> (<var>complex float z</var>)<var><a name="index-crealf-2530"></a></var><br> |
| <blockquote><!-- complex.h --> |
| <!-- ISO --> |
| — Function: long double <b>creall</b> (<var>complex long double z</var>)<var><a name="index-creall-2531"></a></var><br> |
| <blockquote><p>These functions return the real part of the complex number <var>z</var>. |
| </p></blockquote></div> |
| |
| <!-- complex.h --> |
| <!-- ISO --> |
| <div class="defun"> |
| — Function: double <b>cimag</b> (<var>complex double z</var>)<var><a name="index-cimag-2532"></a></var><br> |
| <blockquote><!-- complex.h --> |
| <!-- ISO --> |
| — Function: float <b>cimagf</b> (<var>complex float z</var>)<var><a name="index-cimagf-2533"></a></var><br> |
| <blockquote><!-- complex.h --> |
| <!-- ISO --> |
| — Function: long double <b>cimagl</b> (<var>complex long double z</var>)<var><a name="index-cimagl-2534"></a></var><br> |
| <blockquote><p>These functions return the imaginary part of the complex number <var>z</var>. |
| </p></blockquote></div> |
| |
| <!-- complex.h --> |
| <!-- ISO --> |
| <div class="defun"> |
| — Function: complex double <b>conj</b> (<var>complex double z</var>)<var><a name="index-conj-2535"></a></var><br> |
| <blockquote><!-- complex.h --> |
| <!-- ISO --> |
| — Function: complex float <b>conjf</b> (<var>complex float z</var>)<var><a name="index-conjf-2536"></a></var><br> |
| <blockquote><!-- complex.h --> |
| <!-- ISO --> |
| — Function: complex long double <b>conjl</b> (<var>complex long double z</var>)<var><a name="index-conjl-2537"></a></var><br> |
| <blockquote><p>These functions return the conjugate value of the complex number |
| <var>z</var>. The conjugate of a complex number has the same real part and a |
| negated imaginary part. In other words, ‘<samp><span class="samp">conj(a + bi) = a + -bi</span></samp>’. |
| </p></blockquote></div> |
| |
| <!-- complex.h --> |
| <!-- ISO --> |
| <div class="defun"> |
| — Function: double <b>carg</b> (<var>complex double z</var>)<var><a name="index-carg-2538"></a></var><br> |
| <blockquote><!-- complex.h --> |
| <!-- ISO --> |
| — Function: float <b>cargf</b> (<var>complex float z</var>)<var><a name="index-cargf-2539"></a></var><br> |
| <blockquote><!-- complex.h --> |
| <!-- ISO --> |
| — Function: long double <b>cargl</b> (<var>complex long double z</var>)<var><a name="index-cargl-2540"></a></var><br> |
| <blockquote><p>These functions return the argument of the complex number <var>z</var>. |
| 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 is measured in the usual fashion and ranges from 0 |
| to 2&pi;. |
| |
| <p><code>carg</code> has a branch cut along the positive real axis. |
| </p></blockquote></div> |
| |
| <!-- complex.h --> |
| <!-- ISO --> |
| <div class="defun"> |
| — Function: complex double <b>cproj</b> (<var>complex double z</var>)<var><a name="index-cproj-2541"></a></var><br> |
| <blockquote><!-- complex.h --> |
| <!-- ISO --> |
| — Function: complex float <b>cprojf</b> (<var>complex float z</var>)<var><a name="index-cprojf-2542"></a></var><br> |
| <blockquote><!-- complex.h --> |
| <!-- ISO --> |
| — Function: complex long double <b>cprojl</b> (<var>complex long double z</var>)<var><a name="index-cprojl-2543"></a></var><br> |
| <blockquote><p>These functions return the projection of the complex value <var>z</var> onto |
| the Riemann sphere. Values with a infinite imaginary part are projected |
| to positive infinity on the real axis, even if the real part is NaN. If |
| the real part is infinite, the result is equivalent to |
| |
| <pre class="smallexample"> INFINITY + I * copysign (0.0, cimag (z)) |
| </pre> |
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