MAT314 - Complex Analysis

\\x u. I! u. n I I Problem 6. Find the area of the image of D (0, 1) under the map f (z) = z + g Problem 7. Suppose f is holomorphic on D(0, 1). f(0) = 3 + 42' and |f(z)| S 5 for every 2 6 13(0, 1). Find f'(0). Problem 8. Suppose f E H (C) such that 271' A Show that f E 0. Problem 9. Let f E H (C) with the property f (TENN '19 S Tg , for some 7' > 0 If (z)| S |Rez|*% off the imaginary axis Prove that f is constant. Problem 10. Suppose f E H (C), f (0) = 0, and {z : |f (z)| 0 Show that f (z) = 02\" for some 0 E (C and n E N