COMPLEX(7) Linux Programmers Manual COMPLEX(7)
NAME
complex  basics of complex mathematics
SYNOPSIS
#include
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 Ycoor
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 Xaxis 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
complexonly functions.
EXAMPLE
Your Ccompiler 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 /* for atan */
#include
int
main(void)
{
double pi = 4 * atan(1.0);
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
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20020728 COMPLEX(7)
