prob02 - Problem Set 2 Due February 5th , 2008 1. Consider...

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Problem Set 2 Due February 5 th , 2008 1. Consider following sets: a) A = { z : | Arg z | < π/ 4 } b) B = { z : - 1 < Im z < 1 } c) C = { z : | z | ≥ 1 } d) D = { z : (Re z ) 2 1 } Which of these sets are open? Which are closed? Which are bounded? Which are domains? (No need to prove your statements.) 2. Suppose u ( x,y ) is a real-valued function defined in a domain D . If ∂u ∂x = y and ∂u ∂y = x at all points of D , show that u ( x,y ) = xy + c for some constant c . 3. Prove that if | z 0 | < 1, then z n 0 0 as n → ∞ . 4. Find each of the following limits. (a) lim z
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This note was uploaded on 02/23/2010 for the course MATH 3007 taught by Professor Hou during the Spring '08 term at Columbia.

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