# Section (7) complex

## Name

complex — basics of complex mathematics

## Synopsis

#include <complex.h>

## 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.

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)).

The basic operations are defined on z = a+b*i and w = c+d*i as:

*addition: z+w = (a+c) + (b+d)*i**multiplication: z*w = (a*c − b*d) + (a*d + b*c)*i**division: z/w = ((a*c + b*d)/(c*c + d*d)) + ((b*c − a*d)/(c*c + d*d))*i*

Nearly all math function have a complex counterpart but there are some complex-only functions.

## EXAMPLE

Your C-compiler can work with complex numbers if it
supports the C99 standard. Link with `−lm`

. The imaginary unit is represented
by I.

/* 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 , creal(z), cimag(z)); }

## SEE ALSO

cabs(3), cacos(3), cacosh(3), carg(3), casin(3), casinh(3), catan(3), catanh(3), ccos(3), ccosh(3), cerf(3), cexp(3), cexp2(3), cimag(3), clog(3), clog10(3), clog2(3), conj(3), cpow(3), cproj(3), creal(3), csin(3), csinh(3), csqrt(3), ctan(3), ctanh(3)

## COLOPHON

This page is part of release 5.04 of the Linux * man-pages* project. A
description of the project, information about reporting bugs,
and the latest version of this page, can be found at
https://www.kernel.org/doc/man−pages/.

Copyright 2002 Walter Harms (walter.harmsinformatik.uni-oldenburg.de) %%%LICENSE_START(GPL_NOVERSION_ONELINE) Distributed under GPL %%%LICENSE_END |