Roots of Complex Numbers

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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?
 

Answers and Replies

  • #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
 

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