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-coor-
       dinates.  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 4.16 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/.



                                  2011-09-16                        COMPLEX(7)