SYNOPSIS

DESCRIPTION

EXAMPLE

SEE ALSO

COLOPHON

complex − basics of complex mathematics

**#include
<complex.h>**

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.

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\n", creal(z), cimag(z));

}

**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)

This page is
part of release 3.35 of the Linux *man-pages* project.
A description of the project, and information about
reporting bugs, can be found at
http://man7.org/linux/man-pages/.

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