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manpages_4.04-2_all **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\n", 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 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/.
2011-09-16 COMPLEX(7)