# COMPLEX(7) - Linux man page online | Overview, conventions, and miscellany

Basics of complex mathematics.

Chapter

2011-09-16

**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 func‐ tions.## 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)**

This manual | Reference | Other manuals |
---|---|---|

complex(7) | referred by |
cabs(3) | cacos(3) | cacosh(3) | carg(3) | casin(3) | casinh(3) | catan(3) | catanh(3) | ccos(3) | ccosh(3) | cexp(3) | cexp2(3) | cimag(3) | clog(3) | clog10(3) | clog2(3) | conj(3) | cpow(3) | cproj(3) | creal(3) |

refer to |
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) |