If one defines the $n^{th}$ root of a complex number ($n$ a natural number) so that it coincides with the usual one for the positive real :
- its imaginary part is $\ge 0$
- its real part is the largest among the $n^{th}$ roots whose imaginary part is non-negative.
Is it true that :
$$ \sqrt[m]{\sqrt[n]{x}} = \sqrt[mn]{x}$$