Calcule o determinante abaixo, no qual $\omega =\text{cis}\frac{2\pi }{3}$ e $i=\sqrt{-1}$.$$\left|\begin{array}{cccc}1& \omega & 0& i\\ i& 1& -i& {\omega }^2\\ 1-i& \omega & i-1& 1\\ 0& \omega & 1& i\end{array}\right|$$