Problem 3: Prove that f(z) = –}(z +1/2) is a conformal map from the half-disc {z = x + iy : |z| < 1, y > 0}to the upper half-plane.

(Hint: The equation f(z) = w reduces to the quadratic equation z? + 2wz +1 = 0, which has two distinct roots in C whenever w #±1. This is certainly the case if w E H.)