NAME

SYNOPSIS

DESCRIPTION

EXAMPLE

SEE ALSO

COLOPHON

## NAME

## SYNOPSIS

## DESCRIPTION

## EXAMPLE

## SEE ALSO

## COLOPHON

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 4.04 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
http://www.kernel.org/doc/man−pages/.

© 2018-2020 SourceBinary.com Inc.

Microsoft Windows, XP, Vista are registered trademarks of Microsoft Corporation