**complex**

**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-coor-
dinates. 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));
}
SEE ALSO
**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 project, information about reporting bugs, and the
latest version of this page, can be found at
https://www.kernel.org/doc/man-pages/.
2011-09-16 **COMPLEX(7)**

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