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+.\" Copyright 2002 Walter Harms (walter.harms@informatik.uni-oldenburg.de)
+.\" Distributed under GPL
+.\"
+.TH COMPLEX 5 2002-07-28 "" "complex math"
+.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 \-lm. The imaginary unit is represented by I.
+.sp
+.nf
+/* 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("%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)