complex(7) Miscellaneous Information Manual complex(7)

# 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:

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

# EXAMPLES¶

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));
}
```