# Roots of unity strike again

Algebra Level 4

$\frac { \omega-a_1 }{\omega^2-a_1 }\times\frac { \omega-a_2 }{ \omega^2-a_2 }\times \frac { \omega-a_3 }{ \omega^2-a_3 }\times\frac { \omega-a_4 }{ \omega^2-a_4 }$

If $$1,a_1,a_2,a_3,a_4$$ are the 5th roots of unity and $$\omega$$ is a primitive $$(\omega\neq1)$$ 3rd root of unity, find the value of the expression above.

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