Complex Numbers Question

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funkyducky

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Complex Numbers Question

« on: September 26, 2011, 11:17:17 pm »

0

Could someone work through this question, please? I feel like I'm not seeing something obvious...

$If z = cos \theta + i sin \theta, prove that \frac{1+z}{1-z} = i cot \frac{\theta}{2}$

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I won the GAT: 49/50/50.
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vgardiy

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Re: Complex Numbers Question

« Reply #1 on: September 26, 2011, 11:52:07 pm »

+1

I attached my working.

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Stuff

tony3272

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Re: Complex Numbers Question

« Reply #2 on: September 26, 2011, 11:56:15 pm »

+3

okay for some reason i'm having the greatest difficulty in simplifying the last step but...

$\frac{1+z}{1-z}=\frac{1+cos(x)+isin(x)}{1-cos(x)-isin(x)}$

$=\frac{1+cos(x)+isin(x)}{1-cos(x)-isin(x)}\times\frac{1-cos(x)+isin(x)}{1-cos(x)+isin(x)}$

$=\frac{2sin(x)i}{2-2cos(x)}$

$=\frac{sin(x)i}{1-cos(x)}$

$=cot(\frac{x}{2})i$

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funkyducky

Victorian
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Re: Complex Numbers Question

« Reply #3 on: September 27, 2011, 12:28:47 am »

0

Thanks

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