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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-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)