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Homework Help: URGEN! taking the power of complex exponential

  1. Apr 14, 2013 #1
    1. The problem statement, all variables and given/known data

    e^(i*2pi*1/15) is equal to ( e^(i*2pi) )^(1/15) = (1)^(1/15)=1

    Why this is false?

    2. Relevant equations

    ((A)^(b))^c=A^(b*c)=A^(bc). Why this isn't the case for complex exponential?

    3. The attempt at a solution
     
  2. jcsd
  3. Apr 14, 2013 #2

    Dick

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    Because it isn't. The rule (A^b)^c=A^(bc) doesn't hold for complex exponents. As your example shows.
     
  4. Apr 14, 2013 #3
    But why?
    When I use take the positive integer power of complex exponential, it works. What's the rule?
     
  5. Apr 14, 2013 #4

    Dick

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    If b and c are integers you should be safe. If A is a positive real and one of b or c is an integer, that should also be ok. Otherwise, I think it's dangerous.
     
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