12Spring_hw05_solns - ECE210/211 Spring 2012 Homework 05...

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Unformatted text preview: ECE210/211 - Spring 2012 - Homework 05 solutions 1. Using Euler’s identity ej θ = cos(θ) + j sin(θ), 2e jπ 4 = = 5e π −j 34 = = ￿ π π￿ 2 cos( ) + j sin( ) = 2 4 4 √ √ 2 + j 2. ￿ 3π 3π 5 cos(− ) + j sin(− ) 4 4 √ √ 52 52 − −j 2 2 ￿ ￿√ √￿ 2 2 +j 2 2 ￿√ √￿ 2 2 =5 − −j 2 2 2. First converting rectangular to complex exponentials and then simplifying: R= (2+j 2)3 (5−j 5)7 ∴ |R | = 2 57 , = √ 3 ￿ π ￿3 ( 2 2 ) ej 4 √ 7￿ π ￿7 = ( 5 2 ) e− j 4 ∠R = 3π 3π 8 ej 4 √4 7π 5 7 ( 2 ) e− j 4 = 8 × ej 4 + j 57 × 4 π 2 7π 4 = 2 j 10π 4 57 e = π 2 j 52 57 e = 2 jπ 2 57 e ￿ ￿ ￿ ￿ ￿ ￿ π π 3. Re 10ej 6 ej 2t = Re 10ej (2t+ 6 ) = Re 10 cos(2t + π ) + j 10 sin(2t + π ) = 10 cos(2t + π ) 6 6 6 1 ECE210 - Spring 2012 - Homework 05 Book Problem Solutions Kudeki and Munson, Problems 3.18, 4.1(c), 4.2(c) and 4.3 5. Problem 3.18 from text Solution: 1 6. Problem 4.1(c) from text Solution: 7. Problem 4.2(c) from text 2 Solution: 8. Problem 4.3 from text Solution: 3 ...
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