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For the function $$G(w) = \frac{\sqrt2}{2}-\frac{\sqrt2}{2}e^{iw},$$ show that $$G(w) = -\sqrt2ie^{iw/2} \sin(w/2).$$

Hey everyone, I'm very new to this kind of maths and would really appreciate any help. Hopefully I can get an idea from this and apply it to other similar questions. Thank you.

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    Are you familiar with $e^{i\theta}=\cos\theta+i\sin\theta$?2012-08-20
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    @GerryMyerson Will it work? The `exp(w) -> sin(w/2)` via [Euler's](http://en.wikipedia.org/wiki/Euler%27s_formula) doesn't halve the angle while introduces a cosine. Am I missing something?2012-08-20
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    @Frenz, I just want to know whether OP is familiar with that formula. If not, then the answer posted by Euler is unlikely to be helpful, and we know where an answer has to start. If OP is familiar with that formula, then we can show how to get from there to Euler's answer.2012-08-20
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    @GerryMyerson Oh, right. The worded *familiar* and question mark. :)2012-08-20

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