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 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.

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)