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



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), carg(3), cexp(3), cimag(3), creal(3)

COLOPHON
       This page is part of release 3.22 of the Linux man-pages project.  A description of the project,  and  informa-
       tion about reporting bugs, can be found at http://www.kernel.org/doc/man-pages/.



                                  2009-07-25                        COMPLEX(7)