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## 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));
}

```

```       cabs(3), carg(3), cexp(3), cimag(3), creal(3)
```       This  page  is  part of release 3.24 of the Linux man-pages project.  A
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