1. The problem statement, all variables and given/known data Suppose that |z|<1 and |z-1| < 1. Find arg(z) 2. Relevant equations r = |z| = sqrt(x^2 + y^2) x = r cos (angl) y = r sin (angl) 3. The attempt at a solution I sketched the two planes and the possible values of z lie in the intersection between the unit disc |z| < 1 and the disk shifted one to the right |z - 1| < 1 therefore arg(z) = angle + 2kpi (except the angle can't equal +/- pi/2, +/- 3pi/2, +- pi, +- 2pi) is this right or do I have to compute something?