0132130084_a

# 0132130084_a - 685 APPENDIX A Exercises EA.1 Given 6 8 and...

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Unformatted text preview: 685 APPENDIX A Exercises EA.1 Given , 6 8 and 3 2 2 1 j Z j Z + = − = we have: 3 10 2 1 j Z Z + = + 9 6 2 1 j Z Z − − = − 12 34 18 12 24 16 2 2 1 j j j j Z Z − = − + − = 36 . 02 . 100 18 24 12 16 6 8 6 8 6 8 3 2 / 2 2 1 j j j j j j j j Z Z − − = + − − = − − × + − = EA.2 6 . 10 6 . 10 ) 45 sin( 15 ) 45 cos( 15 45 15 1 j j Z + = + = ∠ = o o o 5 66 . 8 ) 150 sin( 10 ) 150 cos( 10 150 10 2 j j Z − − = − + − = − ∠ = o o o 5 ) 90 sin( 5 ) 90 cos( 5 90 5 3 j j Z = + = ∠ = o o o EA.3 Notice that Z 1 lies in the first quadrant of the complex plane. o 13 . 53 5 ) 3 / 4 arctan( 4 3 4 3 2 2 1 ∠ = ∠ + = + = j Z Notice that Z 2 lies on the negative imaginary axis. o 90 10 10 2 − ∠ = − = j Z Notice that Z 3 lies in the third quadrant of the complex plane. o o o 135 07 . 7 225 07 . 7 )) 5 / 5 arctan( 180 ( 5 5 5 5 2 2 3 − ∠ = ∠ = − − + ∠ + = − − = j Z EA.4 Notice that Z 1 lies in the first quadrant of the complex plane....
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0132130084_a - 685 APPENDIX A Exercises EA.1 Given 6 8 and...

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