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**Unformatted text preview: **. Show that | P ( z ) | ≤ 1 whenever | z | ≤ 1. 5. Let S = { x + iy ∈ C | x,y ∈ [0 , 1] } be the unit square in C . Let f be analytic on a region Ω that contains S . Suppose the following is true: (i) for all z with 0 ≤ Re( z ) ≤ 1, and Im( z ) = 0 or 1, Re f ( z ) = 0; (ii) for all z with Re( z ) = 0 or 1, and 0 ≤ Im( z ) ≤ 1, Im f ( z ) = 0 . Show that f ≡ 0 on Ω. Date : October 29, 2007 (Version 1.1); posted: October 25, 2007; due: October 31, 2007. 1...

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- Fall '07
- Lim
- Math, S. Suppose, C. Let