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Problem 7. Suppose f is holomorphic on D (0, 1). f(0) = 3 + 4i and |f(z)| g 5 for every z 6 13(0, 1). Find f'(0). Problem 8. Suppose f E H (C) such that 27'r A Show that f E 0. Problem 9. Let f E H (C) with the property f (7'39\" d9 5 r1377 , for some 7' > 0 If (z)| g |Rez|_% off the imaginary axis Prove that f is constant. Problem 10. Suppose f E H (C), f (D) = 0, and {z : |f (z)| 0 Show that f (z) = cz" for some 6 E (C and n E N