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Math Help - Expression manipulation

  1. #1
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    Expression manipulation

    p = R^{j\theta} is a complex number where R<1. * is complex conjugation.

    A_1 = \frac{1}{(1-p^*p^{-1})(1-p^{-1})}
    A_2 = \frac{1}{(1-pp*^{-1})(1-p*^{-1})}
    A_3 = \frac{1}{(1-p)(1-p*)}

    Can anyone give a hint at how I can manipulate this expression:

    H_1 = \frac{A_1}{A_3}p^n + \frac{A_2}{A_3}p*^n

    into this expression

    H_2 = \frac{R^{n+2}\sin(\theta(n+1)) - R^{n+1}\sin(\theta(n+2))}{\sin\theta}

    n is discrete and takes on values 0,1,2,...

    I have looked at quite a few trigonometric identities and I have tried to work backwards going from H_2 to H_1 but without any luck. I have verified by simulation that the two expressions are indeed identical
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  2. #2
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    Re: Expression manipulation

    Arrrgh, finally figured it out.
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