Question

HELP!! Which expression is the cube root of -1+itle=" \sqrt{3} " alt=" \sqrt{3} " align="absmiddle" class="latex-formula">

Answer 1

$z^3=-1+i\sqrt3=2e^{i2\pi/3}$

$\implies z=\left(2e^{i2\pi/3}\right)^{1/3}=\begin{cases}2^{1/3}e^{i2\pi/9}\\2^{1/3}e^{i8pi/9}\\2^{1/3}e^{i14\pi/9}\end{cases}$