MATH135_F11_Assignment_9_Solns

MATH135_F11_Assignment_9_Solns - 1 MATH 135 F 2011...

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1 MATH 135 F 2011: Assignment 9 Due: 8:30 AM, Wednesday, 2011 Nov. 30 in the dropboxes outside MC 4066 Write your answers in the space provided. If you wish to typeset your solutions, use the solution template posted on the course web site. Cite any proposition or definition you use. Family Name: First Name: I.D. Number: Section: Mark: (For the marker only.) If you used any references beyond the course text and lectures (such as other texts, discussions with colleagues or online resources), indicate this information in the space below. If you did not use any aids, state this in the space provided. 1. Let z = 3 + 4 i , u = 1 - 2 i and w = 3 i . Express each of the following in standard form. (a) z + 3 u - wi = (3 + 4 i ) + (3 - 6 i ) + (3) = 9 - 2 i (b) zu w = (3 + 4 i )(1 - 2 i )( - 3 i ) = (11 - 2 i )( - 3 i ) = - 6 - 33 i (c) z u = 3 + 4 i 1 - 2 i = 3 + 4 i 1 - 2 i · 1 + 2 i 1 + 2 i = - 5 + 10 i 5 = - 1 + 2 i
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2 2. This question asks you to compute ( 3 + i ) 4 in two ways. Write your answer in standard form. (a) Use the Binomial Theorem. ( 3 + y ) 4 = 4 X r =0 4 r ( 3) 4 - r i r = 4 0 ( 3) 4 - 0 i 0 + 4 1 ( 3) 4 - 1 i 1 + 4 2 ( 3) 4 - 2 i 2 + 4 3 ( 3) 4 - 3 i 3 +
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