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  4. If ω(≠ 1) is a cube root of unity, then |1 1+ i +ω2 ω2 1-i -1 ω2-1 - i - i +ω-1 -1| equals

Q. If $\omega(\neq 1)$ is a cube root of unity, then $\begin{vmatrix}1 & 1+ i +\omega^{2} & \omega^{2} \\ 1-i & -1 & \omega^{2}-1 \\ - i & - i +\omega-1 & -1\end{vmatrix}$ equals

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Solution:

given $3 * x * 2^{-1}=1 \Rightarrow 3 * x=1 * 2$
$\Rightarrow 7\left(\frac{3 x}{3}\right)=7\left(\frac{1.2}{3}\right)$
$ \Rightarrow 3 x=2 \therefore x=2 / 3$

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