# Seth Woolley's Man Viewer

## complex(5) - complex, complex - basics of complex mathematics - man 5 complex

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```COMPLEX(5)                       complex math                       COMPLEX(5)

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(1,8) 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(3,n) 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 <complex.h>
main() {
double pi = 4*atan(1);
complex z = cexp(I*pi);
printf(1,3,1 builtins)("%f+%f*i\n", creal(z), cimag(z));
}