Hello CarmineCortezThe goal is to have 'no' coefficient for - although, of course, the coefficient is really . (Don't forget that, will you?)
The reason this works is that geometrically (to use Mr F's word) is the distance between the points representing the complex numbers and . So if is a constant, will be the distance of the point representing z from a fixed point, which we can call A. This in turn is why the equation (where r is real) represents a circle, centre A, radius .
OK now?
Grandad