hw7-201141 - ± = 1 ⇔ | z | = 1 5 Find all solutions of a...

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Homework 7 1. Express in the form a + bi . a. (1 + i ) 20 . b. 1 - 2 i 2+ i . 2. Solve z 2 - 4 z + (4 + 2 i ) = 0. 3. Describe the sets whose points satisfy the following relations. Which of these sets are regions (i.e., open and connected sets)? a. | z + i | ≤ 1. b. ± ± z - 1 z +1 ± ± = 1. c. | z - 3 | > | z - 2 | . d. 1 z = z . 4. Let a C with | a | < 1, Prove ± ± ± ± a - z 1 - az ± ± ±
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Unformatted text preview: ± = 1 ⇔ | z | = 1 . 5. Find all solutions of a. e z =-i . b. sin z = 0. c. Log z = 1 + i . 6. a. Prove that f ( z ) = Re z is nowhere complex differentiable. b. Prove that f ( z ) = | z | is nowhere complex differentiable. 1...
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