Each of a and c is a positive integer and each of b and d is an integer with b ≥ d.

Determine all possible pairs (a + bi, c + di) of complex numbers whose sum equals their product.

I made myself a little interactive with geometer's sketchpad so I could look at all solutions of
(a + bi) + (c + di) = (a + bi)*(c + di)

The product of the distances of the two numbers from 1+0i is always 1.  I didn't prove this.

The implication is that solutions to the above problem must have distance 1 from 1+0i.  The solutions found in my other post are clearly the only ones that can.

Posted by Jer on 2012-08-30 16:20:59