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Roots and complex numbers

  1. Aug 2, 2005 #1
    There are n nth roots to every complex number (except zero).

    My question: How many "roots" are there when you take a complex number to an irrational or transcendental number. For that matter, how do we define raising a number to an irrational number? How do we define raising a number to a transcendental number?

    Hmm....how is this defined? By a taylor series?

    [tex]
    e^{1/e}
    [/tex]
     
  2. jcsd
  3. Aug 2, 2005 #2

    Hurkyl

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    By definition, in the complexes:

    [tex]z^w := \exp(w \mathop{\mathrm{Log}} z)[/tex]
     
  4. Aug 3, 2005 #3

    HallsofIvy

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    In the complex plane, a number to an irrational (whether transcendental or not) power has an infinite number of values.
     
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