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Math Help - Multivalued functions. Can somebody explain?

  1. #1
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    Multivalued functions. Can somebody explain?

    I really don't understand this:

    The set of values of log(i^{1/2}) is (n+1/4)\pi i, with n \in Z, and that the same is true of \frac{1}{2} log(i), but...

    The set of values of log(i^2) is not the same as the set of values of 2 log(i).
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  2. #2
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    Quote Originally Posted by MathSucker View Post
    I really don't understand this:

    The set of values of log(i^{1/2}) is (n+1/4)\pi i, with n \in Z, and that the same is true of \frac{1}{2} log(i), but...

    The set of values of log(i^2) is not the same as the set of values of 2 log(i).
    I think that the point here is that the square root function, like the logarithm, is multivalued (or 2-valued in the case of the square root). So the set of values of \log(z^{1/2}) means the set of all the logarithms of both square roots of z.

    But when you multiply \log z by 2, you only get half the values of \log(z^2) (the other half come from 2\log(-z)).
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