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: