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If omega is complex cube root of unity, then the value of (1)/(omega) - omega is

March 24, 2026Mathematics

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*a) If $\omega$ is a complex cube root of unity, then the value of $\begin{vmatrix} 1 & \omega \\ \omega & -\omega \end{vmatrix}$ is

Evaluate the determinant.
The determinant of a $2 \times 2$ matrix $\begin{vmatrix} a & b \\ c & d \end{vmatrix}$ is $ad - bc$ .
For the given matrix:
$\begin{vmatrix} 1 & \omega \\ \omega & -\omega \end{vmatrix} = (1)(-\omega) - (\omega)(\omega)$ $= -\omega - \omega^2$
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