160 lines
4.6 KiB
HTML
160 lines
4.6 KiB
HTML
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
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<HTML><HEAD><TITLE>Man page of COMPLEX</TITLE>
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</HEAD><BODY>
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<H1>COMPLEX</H1>
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Section: Linux Programmer's Manual (7)<BR>Updated: 2019-03-06<BR><A HREF="#index">Index</A>
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<A HREF="/cgi-bin/man/man2html">Return to Main Contents</A><HR>
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<A NAME="lbAB"> </A>
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<H2>NAME</H2>
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complex - basics of complex mathematics
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<A NAME="lbAC"> </A>
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<H2>SYNOPSIS</H2>
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<B>#include <<A HREF="file:///usr/include/complex.h">complex.h</A>></B>
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<A NAME="lbAD"> </A>
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<H2>DESCRIPTION</H2>
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Complex numbers are numbers of the form z = a+b*i, where a and b are
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real numbers and i = sqrt(-1), so that i*i = -1.
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<P>
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There are other ways to represent that number.
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The pair (a,b) of real
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numbers may be viewed as a point in the plane, given by X- and
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Y-coordinates.
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This same point may also be described by giving
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the pair of real numbers (r,phi), where r is the distance to the origin O,
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and phi the angle between the X-axis and the line Oz.
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Now
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z = r*exp(i*phi) = r*(cos(phi)+i*sin(phi)).
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<P>
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The basic operations are defined on z = a+b*i and w = c+d*i as:
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<DL COMPACT>
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<DT id="1"><B>addition: z+w = (a+c) + (b+d)*i</B>
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<DD>
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<DT id="2"><B>multiplication: z*w = (a*c - b*d) + (a*d + b*c)*i</B>
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<DD>
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<DT id="3"><B>division: z/w = ((a*c + b*d)/(c*c + d*d)) + ((b*c - a*d)/(c*c + d*d))*i</B>
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<DD>
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</DL>
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<P>
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Nearly all math function have a complex counterpart but there are
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some complex-only functions.
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<A NAME="lbAE"> </A>
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<H2>EXAMPLE</H2>
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Your C-compiler can work with complex numbers if it supports the C99 standard.
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Link with <I>-lm</I>.
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The imaginary unit is represented by I.
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<P>
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/* check that exp(i * pi) == -1 */
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#include <<A HREF="file:///usr/include/math.h">math.h</A>> /* for atan */
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#include <<A HREF="file:///usr/include/stdio.h">stdio.h</A>>
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#include <<A HREF="file:///usr/include/complex.h">complex.h</A>>
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<P>
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int
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main(void)
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{
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<BR> double pi = 4 * atan(1.0);
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<BR> double complex z = cexp(I * pi);
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<BR> printf("%f + %f * i\n", creal(z), cimag(z));
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}
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<A NAME="lbAF"> </A>
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<H2>SEE ALSO</H2>
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<B><A HREF="/cgi-bin/man/man2html?3+cabs">cabs</A></B>(3),
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<B><A HREF="/cgi-bin/man/man2html?3+cacos">cacos</A></B>(3),
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<B><A HREF="/cgi-bin/man/man2html?3+cacosh">cacosh</A></B>(3),
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<B><A HREF="/cgi-bin/man/man2html?3+carg">carg</A></B>(3),
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<B><A HREF="/cgi-bin/man/man2html?3+casin">casin</A></B>(3),
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<B><A HREF="/cgi-bin/man/man2html?3+casinh">casinh</A></B>(3),
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<B><A HREF="/cgi-bin/man/man2html?3+catan">catan</A></B>(3),
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<B><A HREF="/cgi-bin/man/man2html?3+catanh">catanh</A></B>(3),
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<B><A HREF="/cgi-bin/man/man2html?3+ccos">ccos</A></B>(3),
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<B><A HREF="/cgi-bin/man/man2html?3+ccosh">ccosh</A></B>(3),
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<B><A HREF="/cgi-bin/man/man2html?3+cerf">cerf</A></B>(3),
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<B><A HREF="/cgi-bin/man/man2html?3+cexp">cexp</A></B>(3),
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<B><A HREF="/cgi-bin/man/man2html?3+cexp2">cexp2</A></B>(3),
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<B><A HREF="/cgi-bin/man/man2html?3+cimag">cimag</A></B>(3),
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<B><A HREF="/cgi-bin/man/man2html?3+clog">clog</A></B>(3),
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<B><A HREF="/cgi-bin/man/man2html?3+clog10">clog10</A></B>(3),
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<B><A HREF="/cgi-bin/man/man2html?3+clog2">clog2</A></B>(3),
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<B><A HREF="/cgi-bin/man/man2html?3+conj">conj</A></B>(3),
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<B><A HREF="/cgi-bin/man/man2html?3+cpow">cpow</A></B>(3),
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<B><A HREF="/cgi-bin/man/man2html?3+cproj">cproj</A></B>(3),
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<B><A HREF="/cgi-bin/man/man2html?3+creal">creal</A></B>(3),
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<B><A HREF="/cgi-bin/man/man2html?3+csin">csin</A></B>(3),
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<B><A HREF="/cgi-bin/man/man2html?3+csinh">csinh</A></B>(3),
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<B><A HREF="/cgi-bin/man/man2html?3+csqrt">csqrt</A></B>(3),
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<B><A HREF="/cgi-bin/man/man2html?3+ctan">ctan</A></B>(3),
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<B><A HREF="/cgi-bin/man/man2html?3+ctanh">ctanh</A></B>(3)
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<A NAME="lbAG"> </A>
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<H2>COLOPHON</H2>
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This page is part of release 5.05 of the Linux
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<I>man-pages</I>
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project.
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A description of the project,
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information about reporting bugs,
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and the latest version of this page,
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can be found at
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<A HREF="https://www.kernel.org/doc/man-pages/.">https://www.kernel.org/doc/man-pages/.</A>
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<P>
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<HR>
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<A NAME="index"> </A><H2>Index</H2>
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<DL>
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<DT id="4"><A HREF="#lbAB">NAME</A><DD>
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<DT id="5"><A HREF="#lbAC">SYNOPSIS</A><DD>
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<DT id="6"><A HREF="#lbAD">DESCRIPTION</A><DD>
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<DT id="7"><A HREF="#lbAE">EXAMPLE</A><DD>
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<DT id="8"><A HREF="#lbAF">SEE ALSO</A><DD>
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<DT id="9"><A HREF="#lbAG">COLOPHON</A><DD>
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</DL>
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<HR>
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This document was created by
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<A HREF="/cgi-bin/man/man2html">man2html</A>,
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using the manual pages.<BR>
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Time: 00:06:08 GMT, March 31, 2021
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