Expression manipulation

**niaren** · May 21st 2013, 07:26 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, 11:43 PM

Arrrgh, finally figured it out.

Thread: Expression manipulation

LinkBack

Thread Tools

Display

Expression manipulation

Re: Expression manipulation

Similar Math Help Forum Discussions

Limit infina of ratio test and root test

Given a positive test result, find the probability that test taker has the disease.

Lost on Practice Test, teacher gave us test without answers to probems

Help testing these series with any root test or ratio test.

ratio test (series) urgent test tommorow!

Search Tags