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complex - basics of complex mathematics




#include <complex.h>


Complex numbers are numbers of the form 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. Because the point z=(a,b) is on a plane you can also define that point with distance and angle (r,phi). The number z=r*(cos(phi)+i*sin(phi)) can also be described as exponential function z=r*exp(i*phi) as found by Euler.

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.


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 <complex.h>
main() {
double pi = 4*atan(1);
complex z = cexp(I*pi);
printf("%f+%f*i\n", creal(z), cimag(z));


cabs(3), carg(3), cexp(3), cimag(3), creal(3)

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