# Roots of Complex Numbers

1. Dec 18, 2014

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. Dec 18, 2014

### DivergentSpectrum

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.