COMPLEX(7)                (2020-06-09)                 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)

          division: z/w = ((a*c + b*d)/(c*c

          Nearly all math function have a complex counterpart but
          there are some complex-only functions.

     EXAMPLES
          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),

     Page 1                       Plan 9             (printed 5/24/22)

     COMPLEX(7)                (2020-06-09)                 COMPLEX(7)

          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 5.10 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/.

     Page 2                       Plan 9             (printed 5/24/22)