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Simplification with exponentials and imaginary numbers

  1. Nov 7, 2011 #1
    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]
    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.
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Nov 7, 2011 #2


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    whilst it is true
    e^{i \pi} = -1 = e^{-i \pi}

    unless x=2n+1 for some integer n, then
    e^{i \pi x} \neq e^{-i \pi x}

    this makes your last step invalid, though I have not checked the rest
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