Expression manipulation

**niaren** · May 21st 2013, 06:26 AM

$p = R^{j\theta}$ 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

**niaren** · May 21st 2013, 10:43 PM

Arrrgh, finally figured it out.

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Expression manipulation

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