Exercise $13.2. In real coordinates, the complex function z I} 22 takes the form f : it? > 11::2 where f{x,y] = [1'2 ay}. Prove that if gee] e2 {0,0}, men there is an open set V containing {mil} such that f{V] is open and fly : if } t") is a hijection. Exercise grin-.3. Let f be the function described in Exercise 3.6.2. For both of the points {LB} and [1,I|]], find a set if that satisfies H1ose conditions and compute {fly} I. Theorem 7.6.1 (The inverse function theorem). Suppose that U C " is open and that f : U - R". If f is continuously differentiable on U and Df (c) is invertible for some point c E U, then there is an open set V C U containing the point c such that (a) fly : V - f(V) is a bijection, (b) f(V) is open, (c) (fly ) 1 is continuously differentiable, and (d) D(flv) (f(c)) = (Df(c)) -1