assgt4 - (i) ( 5 marks ) n X k =1 z k ! = n X k =1 z k (ii)...

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MATH 407-10a, Assignment 4 Guidelines Answer the questions in the space provided; you may write on both sides of the paper. Put the names of all group members in the top right corner. You may append additional sheets as needed. Please staple all sheets together before submission. Due: Thursday, Feb 4th (in class) 1. Suppose that n is a fixed positive integer, and that z 1 ,...,z n are complex numbers. Use the principle of mathematical induction to prove each of the following:
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Unformatted text preview: (i) ( 5 marks ) n X k =1 z k ! = n X k =1 z k (ii) ( 5 marks ) ( z 1 z 2 z n ) = z 1 z 2 z n 2. ( 10 marks ) Let N be a xed positive integer. Consider the polynomial P ( z ) := N X k =0 a k z k , z C , where every a k , 0 k N , is a real number. Prove that a complex number is a root of P if and only if is also a root of P ; that is, prove that P ( ) = 0 if and only if P ( ) = 0....
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This note was uploaded on 03/08/2010 for the course MATH 407 taught by Professor Staff during the Fall '08 term at Texas A&M.

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