Hi, I'm using euler's identity : exp(i∏) = exp (-i∏) = -1 to simplify the equation after integrating it.(adsbygoogle = window.adsbygoogle || []).push({});

[PLAIN]http://img443.imageshack.us/img443/5504/captureikm.jpg [Broken]

Note: the equation to be integrated is exp(0.5it) + exp(-0.5it) and they have simplified it, it was actually a cos(0.5t) function and the 1/2 from cos(t) = 0.5[ exp(it) + exp(-it) ] isn't included.

However, after trying I got the numerator to be 0, because of the exp(i∏) = exp (-i∏) problem.

Letting x and y be any variable,

exp(i∏ x) - exp(i∏ y) - [ exp(i(-∏) x) - exp(i(-∏) y) ]

= exp(i∏ x) - exp(i(-∏) x) - exp(i∏ y) + exp(i(-∏) y) ---------(rearranging)

= exp(i∏ x) - exp(i(∏) x) - exp(i∏ y) + exp(i(∏) y) -----------(since exp(i∏) = exp (-i∏))

= 0

Please help me, thank you very much.

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# Simplification with exponentials and imaginary numbers

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