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## NAME

complex- basics ofcomplexmathematics## 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))*iNearly 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),carg(3),cexp(3),cimag(3),creal(3)COLOPHON

This page is part of release 3.27 of the Linux man-pages project. A description of the project, and information about reporting bugs, can be found at //www.kernel.org/doc/man-pages/. 2009-07-25 COMPLEX(7)

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