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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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    @GerryMyerson Oh, right. The worded *familiar* and question mark. :)2012-08-20

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Use the definition for the complex sine: $ \sin(z)=\frac{ e^{iz}-e^{-iz} } {2i} $ Thus, $-\sqrt{2}ie^{i\frac{w}{2}}\sin\frac{w}{2} =-\sqrt{2}ie^{i\frac{w}{2}}(\frac{1}{2i}(e^{i\frac{w}{2}} - e^{-i\frac{w}{2}})) $

Now simplify to get your result.

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    @FrenzY DT. Thanks, I was told that if i use the complex sine for this, it = -isinh(i*w/2). But im not really sure about that and where to go from here. Sorry if this is obvious to you.2012-08-21