Please solve this complex analysis problem, especially part c please. Cauchy inequalities need to be used.

15. Use the Cauchy inequalities or the maximum modulus principle to solve the following problems: (a) Prove that if f is an entire function that satises sup |f(z)| S ARI\" +B |z|=R for all R > 0, and for some integer k: 2 0 and some constants A, B > 0, then f is a polynomial of degree 3 k. (b) Show that if f is holomorphic in the unit disc, is bounded, and converges uniformly to zero in the sector 9 1, then f = O. (G) Let wl, . . . ,wn be points on the unit circle in the complex plane. Prove that there exists a point z on the unit circle such that the product of the distances from 2 to the points 1113-, 1 S j 5 n, is at least 1. Conclude that there exists a point w on the unit circle such that the product of the distances from w to the points 1w, 1 S j S n, is exactly equal to 1. (d) Show that if the real part of an entire function f is bounded, then f is constant