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((e^(i*pi))^x)-((e^(-i*pi))^x)=0? how?

  1. May 24, 2012 #1
    Can someone help explain this? Wolfram says it is zero but I don't know why?
     
  2. jcsd
  3. May 24, 2012 #2
  4. May 24, 2012 #3
    Ok I know eulers but how does 1^x - (-1)^x = 0?
     
  5. May 24, 2012 #4
    That's ##\left(-1\right)^x-\left(-1\right)^x##, after some simplification.
     
  6. May 24, 2012 #5

    Mentallic

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    [tex]e^{ix}=\cos(x)+i \sin(x)[/tex] hence after plugging [itex]x=-\pi[/itex] we get [tex]e^{-i\pi}=\cos(-\pi) +i \sin(-\pi)[/tex] and recall that [itex]\cos(-x)=\cos(x)[/itex] and [itex]\sin(-x)=-\sin(x)[/itex] thus we have [tex]e^{-i\pi}=\cos(\pi)-i\sin(\pi)=-1-0i=-1[/tex] while similarly, [tex]e^{i\pi}=\cos(\pi)+i\sin(\pi)=-1+0i=-1[/tex]
     
  7. May 24, 2012 #6
    Ok I see now thx
     
  8. May 26, 2012 #7

    haruspex

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    ((e^(i*pi))^x)-((e^(-i*pi))^x) does not reduce to 1^x - (-1)^x.
    It reduces to (-1)^x - (-1)^x.
     
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