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Math Help - Find the principal value

  1. #1
    Junior Member universalsandbox's Avatar
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    Find the principal value

    How do you find the principal value of 1^(3i)?
    As well, (1-i*sqrt(3))^(1+pi*i)


    Thanks
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  2. #2
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    Quote Originally Posted by universalsandbox View Post
    How do you find the principal value of 1^(3i)?
    As well, (1-i*sqrt(3))^(1+pi*i)


    Thanks
    For z\not = 0 write z=re^{i\theta}, \theta \in (-\pi,\pi].
    Define, \log z = \ln (r) + i \theta.

    Define, a^b = e^{b\log a}, a\not = 0 for a,b\in \mathbb{C}.
    Can you solve your problem now?
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