If $\omega$ is a cube root of unity, then the value of $\left(1-\omega^8\right)\left(1-\omega^4\righ

Question

If $\omega$ is a cube root of unity, then the value of $\left(1-\omega^8\right)\left(1-\omega^4\right)\left(1-\omega^2\right)(1-\omega)$ is

Professor PC Thomas Classes · Answer

Using $\omega^3 = 1$, roots become $(1-\omega^2)(1-\omega)(1-\omega^2)(1-\omega) = [(1-\omega)(1-\omega^2)]^2 = 3^2 = 9$.