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Unformatted text preview: Problem 6. (10) Let r &gt; 0 and let z be a point in C . Suppose that f is analytic on and inside the circle | z-z | = r . Use the Cauchy integral formula to show that f ( z ) = 1 2 Z 2 f ( z + re it ) d t. This is known as the mean value property . Problem 7. (5 each, 10 total) (a) Let be the arc of the circle | z | = 1 that is parametrized by z ( ) = e i for 0 6 6 / 2. Show that for every z on , we have | Log( z ) | 6 / 2. (b) Show that Z Log( z ) d z 6 2 4 . 1...
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This note was uploaded on 10/03/2011 for the course MATH 3364 taught by Professor Staff during the Spring '08 term at University of Houston.
- Spring '08