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Homework Help: Solve Z^60

  1. Jan 21, 2008 #1

    nicksauce

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    1. The problem statement, all variables and given/known data
    Evaluate [tex]z^{60}[/tex], where [tex]z = -1 + i\sqrt{3}[/tex]


    2. Relevant equations



    3. The attempt at a solution
    [tex]z = 2(\cos(\frac{2\pi}{3}) + i\sin(\frac{2\pi}{3})[/tex]
    [tex]z^{60} = 2^{60}(\cos(40\pi) + i\sin(40\pi))[/tex]
    [tex]z^{60} = 2^{60}[/tex]

    Is this right? Maple doesn't seem to agree.
     
  2. jcsd
  3. Jan 21, 2008 #2
    Unless I'm misremembering the various formulas involved, that seems correct. What is Maple giving as the answer?
     
  4. Jan 21, 2008 #3

    nicksauce

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    z := -1 + I sqrt(3)
    a := z^60
    evalf(a, 5)
    1.1544 10^18 - 8.5175 10^14 I

    Perhaps the imaginary part is just due to some kind of rounding error?
     
  5. Jan 21, 2008 #4
    Probably so. After all, you're dealing with some pretty big numbers and using, I'm guessing, 5 digits. Bound to introduce a pretty big error.
     
  6. Jan 21, 2008 #5

    nicksauce

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    I'm quite surprised maple wouldn't use exact methods, such as I used here, to calculate such numbers!
     
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