# complex(7) — Linux manual page

```complex(7)          Miscellaneous Information Manual          complex(7)
```

## NAME         top

```       complex - basics of complex mathematics
```

## LIBRARY         top

```       Math library (libm, -lm)
```

## SYNOPSIS         top

```       #include <complex.h>
```

## DESCRIPTION         top

```       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.
```

## EXAMPLES         top

```       Your C-compiler can work with complex numbers if it supports the
C99 standard.  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),