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)*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 +
Nearly all math function have a complex counterpart but there are some
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 */
double pi = 4 * atan(1.0);
double complex z = cexp(I * pi);
printf("%f + %f * i\n", creal(z), cimag(z));