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Unformatted text preview: Complex Variables
Spring 2011 Exercise 1. Deﬁne f (z ) = Assignment 8.1
Due October 24
√ reiθ/2 where z = reiθ with −π ≤ θ < π . Let R denote the rectangle with vertices i, −i, 2 − i and 2+ i. Use Lemma 2.3.4 to help you evaluate f (z ) dz .
R Exercise 2. Let G be the region of textbook Exercise 2.3.5. Use Cauchy’s Theorem for a
Rectangle to prove that if f is analytic on G and on its boundary ∂G, then f (z ) dz = 0.
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This note was uploaded on 02/29/2012 for the course MATH 4364 taught by Professor Ryandaileda during the Fall '11 term at Trinity University.
- Fall '11