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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-coordinates.  This same point may also be de‐
       scribed 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  func‐
       tions.

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),  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/.



                                             2020-06-09                                   COMPLEX(7)