COMPLEX
Section: Linux Programmer's Manual (7)
Updated: 20110916
Index
Return to Main Contents
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
Ycoordinates.
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 <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)
COLOPHON
This page is part of release 4.15 of the Linux
manpages
project.
A description of the project,
information about reporting bugs,
and the latest version of this page,
can be found at
https://www.kernel.org/doc/manpages/.
Index
 NAME

 SYNOPSIS

 DESCRIPTION

 EXAMPLE

 SEE ALSO

 COLOPHON

This document was created by
man2html,
using the manual pages.
Time: 02:06:06 GMT, September 25, 2018