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 5.05 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 https://www.kernel.org/doc/man-pages/.

                                            2019-03-06                                 COMPLEX(7)