[Go to CFHT Home Page] Man Pages
Back to Software Index  BORDER=0Manpage Top Level
    COMPLEX(7) manual page Table of 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 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) ).

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 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 3.78 of the Linux man-pages project. A description of the project, information about reporting bugs, and the latest version of this page, can be found at http://www.kernel.org/doc/man-pages/.

Table of Contents