man > COMPLEX

complex(7)                        Miscellaneous Information Manual                        complex(7)

NAME
       complex - basics of complex mathematics

LIBRARY
       Math library (libm, -lm)

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.  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)

Linux man-pages 6.7                          2023-10-31                                   complex(7)