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),  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 4.09 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)

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