- #1

JieXian

- 6

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Hi, I'm using euler's identity : exp(i∏) = exp (-i∏) = -1 to simplify the equation after integrating it.

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

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) ---------

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

= 0

Please help me, thank you very much.

[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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