Question 10 (8 marks) It is easy to show that if f : C - C is analytic on all of C and f(2) is real for all z e C, then f is a constant, i.e., there is a constant A such that f(2) = A for all z e C. For any function h : C - C, we define h : C - C by h(z) = h(2) for all z e C. Use the above fact to solve the following: (a) If both g and g are analytic on all of C, then g is a constant. (b) If g is analytic on all of C and (g(2) |2 = 2021 for all 2 c C. then g is a constant