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Math Help - complex manipulation?????

  1. #1
    Member i_zz_y_ill's Avatar
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    complex manipulation?????

    Q show that 1/(1-e^jx) = 1/2(1+jcot(x/2)) where x=theta,sorry bwt x

    the first line of woking is to answer ( e^-jx/2 ) / ( (e^-jx/2 - e^jx/2 )

    but how does 1 = e^-jx/2

    could someone show me how to get ans pls???

    Last edited by i_zz_y_ill; May 3rd 2008 at 12:57 PM. Reason: igot it sorry to bother
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  2. #2
    Eater of Worlds
    galactus's Avatar
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    Two handy identites to know are:

    sin{\theta}=\frac{e^{i{\theta}}-e^{-i{\theta}}}{2i}

    and cos{\theta}=\frac{e^{i{\theta}}+e^{-i{\theta}}}{2}

    e^{i{\theta}}=cos{\theta}+isin{\theta}

    e^{-i{\theta}}=cos{\theta}-isin{\theta}

    Another one handy to know is the identity tan(\frac{\theta}{2})=\frac{1-cos{\theta}}{sin{\theta}}

    So, you have \frac{1}{1-e^{-i{\theta}}}=\frac{1}{1-cos{\theta}+isin{\theta}}
    Last edited by galactus; May 3rd 2008 at 01:21 PM.
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