1. The problem statement, all variables and given/known data Let a, b in R, not both zero. Find c, d in R such that (a+bi)^-1 = c+di 2. Relevant equations i^2=-1 R is the set of all real numbers 3. The attempt at a solution I have a feeling I'm approaching this problem incorrectly but: 1 = (a + bi)(c + di) =ac + adi + cbi + bdi^2 but i^2=-1 so 1 = ac - bd + (ad + bc)i^2 This is as far as I've attempted becuase I realised that my solution really isn't going anywhere. Maybe someone could just give me a hint to start me off on the right track.