.\" Copyright 2002 Walter Harms (walter.harms@informatik.uni-oldenburg.de)
.\" Distributed under GPL
.\"
.TH COMPLEX 7 2002-07-28 "" "Linux Programmer's Manual"
.SH NAME
complex \- basics of complex mathematics
.SH SYNOPSIS
.B #include <complex.h>
.SH 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.
.br
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)).
.PP
The basic operations are defined on z = a+b*i and w = c+d*i as:
.TP
.B addition: z+w = (a+c) + (b+d)*i
.TP
.B multiplication: z*w = (a*c \- b*d) + (a*d + b*c)*i
.TP
.B division: z/w = ((a*c + b*d)/(c*c + d*d)) + ((b*c \- a*d)/(c*c + d*d))*i
.PP
Nearly all math function have a complex counterpart but there are
some complex only functions.
.SH EXAMPLE
Your C-compiler can work with complex numbers if it supports the C99 standard.
Link with \fI-lm\fP.
The imaginary unit is represented by I.
.sp
.nf
/* check that exp(i * pi) == \-1 */
#include <math.h>        /* for atan */
#include <complex.h>

int
main(void)
{
    double pi = 4 * atan(1);
    complex z = cexp(I * pi);
    printf("%f + %f * i\\n", creal(z), cimag(z));
}
.fi
.SH "SEE ALSO"
.BR cabs (3),
.BR carg (3),
.BR cexp (3),
.BR cimag (3),
.BR creal (3)