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[linuxjm/LDP_man-pages.git] / original / man7 / complex.7

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-.\" Copyright 2002 Walter Harms (walter.harms@informatik.uni-oldenburg.de)
-.\"
-.\" %%%LICENSE_START(GPL_NOVERSION_ONELINE)
-.\" Distributed under GPL
-.\" %%%LICENSE_END
-.\"
-.TH COMPLEX 7 2011-09-16 "" "Linux Programmer's Manual"
-.SH NAME
-complex \- basics of complex mathematics
-.SH SYNOPSIS
-.B #include <complex.h>
-.SH DESCRIPTION
-Complex numbers are numbers of the form z = a+b*i, where a and b are
-real numbers and i = sqrt(\-1), so that i*i = \-1.
-.br
-There are other ways to represent that number.
-The pair (a,b) of real
-numbers may be viewed as a point in the plane, given by X- and
-Y-coordinates.
-This same point may also be described by giving
-the pair of real numbers (r,phi), where r is the distance to the origin O,
-and phi the angle between the X-axis and the line Oz.
-Now
-z = r*exp(i*phi) = r*(cos(phi)+i*sin(phi)).
-.PP
-The basic operations are defined on z = a+b*i and w = c+d*i as:
-.TP
-.B addition: z+w = (a+c) + (b+d)*i
-.TP
-.B multiplication: z*w = (a*c \- b*d) + (a*d + b*c)*i
-.TP
-.B division: z/w = ((a*c + b*d)/(c*c + d*d)) + ((b*c \- a*d)/(c*c + d*d))*i
-.PP
-Nearly all math function have a complex counterpart but there are
-some complex-only functions.
-.SH EXAMPLE
-Your C-compiler can work with complex numbers if it supports the C99 standard.
-Link with \fI\-lm\fP.
-The imaginary unit is represented by I.
-.sp
-.nf
-/* check that exp(i * pi) == \-1 */
-#include <math.h>        /* for atan */
-#include <stdio.h>
-#include <complex.h>
-
-int
-main(void)
-{
-    double pi = 4 * atan(1.0);
-    double complex z = cexp(I * pi);
-    printf("%f + %f * i\\n", creal(z), cimag(z));
-}
-.fi
-.SH SEE ALSO
-.BR cabs (3),
-.BR cacos (3),
-.BR cacosh (3),
-.BR carg (3),
-.BR casin (3),
-.BR casinh (3),
-.BR catan (3),
-.BR catanh (3),
-.BR ccos (3),
-.BR ccosh (3),
-.BR cerf (3),
-.BR cexp (3),
-.BR cexp2 (3),
-.BR cimag (3),
-.BR clog (3),
-.BR clog10 (3),
-.BR clog2 (3),
-.BR conj (3),
-.BR cpow (3),
-.BR cproj (3),
-.BR creal (3),
-.BR csin (3),
-.BR csinh (3),
-.BR csqrt (3),
-.BR ctan (3),
-.BR ctanh (3)
-.SH COLOPHON
-This page is part of release 3.79 of the Linux
-.I man-pages
-project.
-A description of the project,
-information about reporting bugs,
-and the latest version of this page,
-can be found at
-\%http://www.kernel.org/doc/man\-pages/.