Provided by: manpages_4.15-1_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));
}

```

#### SEEALSO

```       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 4.15 of the Linux man-pages project.  A  description  of  the