complex - basics of complex mathematics

       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)*imultiplication:z*w=(a*c-b*d)+(a*d+b*c)*idivision: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.

       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));
       }

       Math library (libm, -lm)

       complex - basics of complex mathematics

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 6.9.1                              2024-06-15                                         complex(7)

#include<complex.h>