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set_6_problem - Problem Set 6 MMAE 501 Engineering Analysis...

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Problem Set # 6 MMAE: 501 Engineering Analysis I Kevin W. Cassel Mechanical, Materials and Aerospace Engineering Department Illinois Institute of Technology 10 West 32nd Street Chicago, IL 60616 [email protected] Problem Reference Problem # 1: Jeffrey, Section 1.2, Problem 7 Problem # 2: Jeffrey, Section 1.2, Problem 11 Problem # 3: Jeffrey, Section 1.4, Problem 18 Problem # 4: Jeffrey, Section 13.1, Problem 11 Problem # 5: Jeffrey, Section 13.2, Problem 12 Problem # 6: Jeffrey, Section 13.2, Problem 35 Problem # 7: Jeffrey, Section 13.2, Problem 36 Problem # 8: Problem # 9: Jeffrey, Section 13.3, Problem 4 Problem # 10: Jeffrey, Section 13.3, Problem 11 Problem # 11: Jeffrey, Section 13.3, Problem 14 c 2007 Kevin W. Cassel 1
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Problem # 1 Given that z = 1 is a root, find the other two roots of 2 z 3 - z 2 + 3 z - 4 = 0 . Problem # 2 Given that u = 2 + 3 i, v = 1 - 2 i, w = - 3 - 6 i , find | u + v | , u + 2 v, u - 3 v + 2 w, uv, uvw, | u/v | , v/w . Problem # 3 Use the factorization ( 1 - z n +1 ) = (1 - z ) ( 1 + z + z 2 + · · · + z n ) , z 6 = 1 , with z = e = exp( ) to show that n X k =1 exp( ikθ ) = exp( inθ ) - 1 1 - exp( - ) .
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