# 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**

# 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)