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Identity for exponential function with imaginary arguments

  1. Jan 15, 2009 #1
    I have seen the following identity used.
    Exp[iw/2]-Exp[iw/2]=Exp[iw]-1
    I can't find this in any book and I can't prove it myself.
    The left side equals 2isin(w/2)
    The right side equals cos(w)+isin(w)-1
    On the face of it, that seems to make the identity absurd
    How can one go about proving such an identity? Or is it wrong?
     
  2. jcsd
  3. Jan 15, 2009 #2

    tiny-tim

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    Welcome to PF!

    Hi ParityCheck ! Welcome to PF! :smile:

    (eiw/2 - e-iw/2)eiw/2 = eiw - 1 :wink:
     
  4. Jan 15, 2009 #3
    Thanks. I was making it way too complicated with trig identities and series and.....
     
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