# complex(7) [centos man page]

```COMPLEX(7)						     Linux Programmer's 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:

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
", creal(z), cimag(z));
}

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 3.53 of the Linux man-pages project.  A description of the project, and information about reporting bugs,  can
be found at http://www.kernel.org/doc/man-pages/.

2011-09-16								COMPLEX(7)```

## Check Out this Related Man Page

```COMPLEX(7)						     Linux Programmer's 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:

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
", creal(z), cimag(z));
}