1. The problem statement, all variables and given/known data Show that the inversion mapping w = f(z) = 1/z maps the circle |z - 1| = 1 onto the vertical line x = 1/2. 2. Relevant equations 3. The attempt at a solution z = a + ib w = x + yi = a^2/(a^2 + b^2) + ib^2/(a^2 + b^2) |z - 1| = |(a -1) + ib | = 1 (a - 1)^2 + b^2 = 1 a^2 + b^2 = 2ab Not sure what to do afterwards.