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Simple exponential question

  1. Dec 17, 2007 #1
    I'm currently learning complex analysis, and there's something I can't quite get...

    Usually:
    Code (Text):
    e^2 * e^3 = e^(2+3) = e^5
    So why is that:
    Code (Text):
    e^(i*PI*t) * e^(i*PI) = -e^(i*PI*t)
    ?

    I was able to get the solution from:
    Code (Text):
    e^(i*PI*t) * e^(i*PI) =
      = (Cos(PI*t) + iSin(PI*t)) * (Cos(PI) + iSin(PI)) =
      = (Cos(PI*t) + iSin(PI*t)) * (-1) =
      = -e^(i*PI*t)
    But, what am I missing? :redface:

    Thanks!
     
  2. jcsd
  3. Dec 17, 2007 #2
    I don't think you are missing anything, it is just another way to say the same thing.

    [tex]
    e^{i\pi t}e^{i\pi}=e^{i\pi t+i\pi}=-e^{i\pi t}
    [/tex]

    Because as you have derived yourself
    [tex]
    e^{i\pi}=-1
    [/tex]
     
  4. Dec 17, 2007 #3
    Hm, I see.

    The first time I came across this I just assumed:
    [tex]
    e^{i\pi t}e^{i\pi}=e^{i\pi t+i\pi}=e^{i\pi (t+1)}
    [/tex]
    was the simplest way it could get.

    Well, thanks again! :smile:
     
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