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Appendix A - APPENDIX A Exercises EA.1 Given Z 1 = 2 j 3...

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1 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 . 0 02 . 0 100 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. ) 45 exp( 14 . 14 45 14 . 14 ) 10 / 10 arctan( 10 10 10 10 2 2 1 o o j j Z = = + = + = Notice that Z 2 lies in the second quadrant of the complex plane.
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