1. Let f(0,2) -> C be a holomorphic function. Suppose that f is real-valued

on the set {|z| = 1}. Show that f is a constant.

2. Can you find a 1-1 conformal map from {z complex number | 0 < |z| < 1}

onto the annulus X = {z complex | 1 < |z| < 2}.

Thanks for helping.