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Homework Help: Eulers Identity

  1. May 7, 2010 #1
    1. The problem statement, all variables and given/known data
    Okay, yesterday in class my teacher gave me this identity [tex]e^{i\pi }+1=0[/tex]
    and she wants me to rearrange the numbers around, so I can get this [tex]i^{i}= e^{-\frac{\pi}{2}}[/tex]


    2. Relevant equations and 3. The attempt at a solution
    I know that if Isolate the 1 to the other side and take the square root of each sides I will have this [tex]\sqrt{e^{i\pi }}= \sqrt{-1}[/tex]
    But this is the question what do I do after that ?
     
    Last edited: May 7, 2010
  2. jcsd
  3. May 7, 2010 #2

    jbunniii

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    Do you know another way to write

    [tex]\sqrt{e^{i \pi}}[/tex]?

    Do you know another way to write

    [tex]\sqrt{-1}[/tex]?
     
  4. May 7, 2010 #3

    tiny-tim

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    Hi xvtsx! :smile:

    (have a pi: π and try using the X2 tag just above the Reply box :wink:)

    Raise each side of your last equation to the power of i. :smile:
     
  5. May 7, 2010 #4
    Hmm.. do I raise to the power of i after I change the square root for [tex]\frac{1}{2}[/tex] and multiple it with [tex]iπ[/tex] ?
     
    Last edited: May 7, 2010
  6. May 7, 2010 #5

    tiny-tim

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    (what happened to that π i gave you? :redface:)

    Yes, (eiπ/2)i = … ? :smile:
     
  7. May 7, 2010 #6
    sorry for the pi part, but I use the latex editor and it only gaves that one xD.. thanks by the way. :)
     
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