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Find

$$\mathrm{Re}\bigg(\frac{\cos(x+iy)}{(1-e^{ix})}\bigg)$$

and

$$\mathrm{Im}\bigg(\frac{\cos(x+iy)}{(1-e^{ix})}\bigg)$$

Please help I've been trying for some time now...

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two things: first please learn to use Latex. I've fixed the post for you but its a lot neater to read when it's pretty. ;) second. can you show us what you've tried so far? maybe that will help us help you. –  franklin May 1 '13 at 20:09

2 Answers 2

up vote 0 down vote accepted

Multiply the numerator and denominator by $1-e^{-ix}$ and you get a denominator that is real. Then you just have to find the real and imaginary parts of $\cos(x+iy)(1-e^{-ix})$.

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Thankyou, this works but is rather messy any other suggestions to simplify the algebra? –  Anon May 1 '13 at 20:39
    
There's no way to not make it messy, I don't think. It's a messy problem. –  Thomas Andrews May 1 '13 at 20:43

Hint: Use $$\cos (z) = \frac{e^{iz}+e^{-iz}}{2}$$

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