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Roots of Complex Numbers

  1. Dec 18, 2014 #1
    Within the context of real numbers, the square root function is well-defined; that is, the function ##f## defined by:
    ##f(x) = \sqrt{x}##
    Refers to the principal root of any real number x.
    Is it true that this is not the case when dealing with complex numbers? Does ##\sqrt{z}##, where ##z ∈ ℂ##, represent more than one value?
     
  2. jcsd
  3. Dec 18, 2014 #2
    It depends more on how you define nth root, not so much whether the input is a complex number.
    If you define n√x as the inverse function of xn, then yes, there is more than one value, and infact more than one inverse function.
    more reading youll enjoy:
    http://en.wikipedia.org/wiki/Root_of_unity
     
  4. Dec 18, 2014 #3

    PeroK

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