# Manual Reference Pages  - COMPLEX (7)

### NAME

complex - basics of complex mathematics

Synopsis
Description
Example

### 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 <complex.h>
main() {
double pi = 4*atan(1);
complex z = cexp(I*pi);
printf("%f+%f*i\n", creal(z), cimag(z));
}

```

### SEE ALSO

cabs(3), carg(3), cexp(3), cimag(3), creal(3)

 COMPLEX (7) 2002-07-28
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