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Homework Help: Complex power raised over real number.

  1. Aug 22, 2012 #1
    1. I actually dont know if such kind of operation is even allowed.

    A friend of mine raised this question, that can we raise a complex power over a real number. I solved it this way. Is this correct?

    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
    Last edited by a moderator: Aug 22, 2012
  2. jcsd
  3. Aug 22, 2012 #2


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    Yes, that's fine.
  4. Aug 22, 2012 #3
    Yes, you did it correctly. I am not quite sure approximating the transcandental functions with decimals, but I suppose that's fine.
  5. Aug 22, 2012 #4

    Ray Vickson

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    Your method is OK, but if you plan to use the results in further numerical computations, you should keep more digits of accuracy; nowadays, in this computer age, there is no barrier to retaining more digits. For example, it might be better (depending on future uses) to write
    [tex]3^{5i} = e^{i 5 \ln 3 } = \cos(5 \ln 3) + i \sin(5 \ln 3) \doteq
    0.7037573 - 0.7104404 i\, . [/tex]

  6. Aug 22, 2012 #5
    Yeah this is obviously much better, I was just looking whether it is even possible or not as none of the books I use has such question.
    Would be awesome if you could suggest some good book for complex number (pre collage).
  7. Aug 23, 2012 #6


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    Are you also taking into account that there are infinitely-many solutions depending

    on your choice of branch/argument?
  8. Aug 24, 2012 #7
    well thats obvious, isnt it? trigo fn is periodic, i just stayed in principle branch
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