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# hw5 - R γ f f dz is an even multiple of 2 πi for f z =...

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Complex Analysis Spring 2001 Homework V Due Friday May 26 1. Conway, chapter 4, section 5, problem 7. 2. Conway, chapter 4, section 5, problem 9. 3. Conway, chapter 4, section 6, problem 6. 4. Conway, chapter 4, section 6, problem 10. 5. Show that an analytic branch of 1 - z 2 can be defined in any region G such that 1 and - 1 lie in the same component of the complement, by proving that
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Unformatted text preview: R γ f f dz is an even multiple of 2 πi for f ( z ) = 1-z 2 for every closed curve γ in G. 6. Show how the proof of Theorem 7.2 can be modiﬁed to evaluate Z γ f ( z ) f ( z ) h ( z ) dz where f, γ, and G are as in Theorem 7.2, and h ( z ) is analytic on G ....
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