COMPLEX(7)                Linux Programmer's Manual               COMPLEX(7)

NAME         top

       complex - basics of complex mathematics

SYNOPSIS         top

       #include <complex.h>

DESCRIPTION         top

       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 +

       Nearly all math function have a complex counterpart but there are
       some complex-only functions.

EXAMPLE         top

       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>

           double pi = 4 * atan(1.0);
           double complex z = cexp(I * pi);
           printf("%f + %f * i\n", creal(z), cimag(z));

SEE ALSO         top

       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         top

       This page is part of release 4.08 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

                                 2011-09-16                       COMPLEX(7)