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: