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Unformatted text preview: i i . Express your solutions in the form + i . (b) Find all values of [0 , 2 ) for which the following limit exists lim r e re i . 5. Let a ,...,a 4 R . Suppose the polynomial equation a 4 z 4 + ia 3 z 3 + a 2 z 2 + ia 1 z + a = 0 has a root given by z = + i . Find another root of the equation. Your answer should only depend on , . Date : September 5, 2009 (Version 1.0); due: September 11, 2009. 1 6. Let z n ,w n C for every n N . Show that (a) If n =1 z n and n =1 w n are both convergent, then so is X n =1 z n + w n for any , C . (b) If n =1 z n is convergent, then lim n z n = 0 . (c) If n =1 | z n | is convergent, then so is n =1 z n . 2...
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- Fall '07