Exercise 2. Let G be a region in the plane that does not contain zero and let G* be the set of all points z such that there is a point w in G where z and w are symmetric with respect to the circle |El = 1. (See III. 3.17.) (a) Show that G* = {z : (1/z) E G). (b) If f : G - C is analytic, define f* : G* - C by f*(z) = f(1/z). Show that f* is analytic. (c) Suppose that G = G* and f is an analytic function defined on G such that f(z) is real for z in G with Izl = 1. Show that f = f*. (d) Formulate and prove a version of the Schwarz Reflection Principle where the circle |El = 1 replaces R. Do the same thing for an arbitrary circle