Let $\omega$ be a nonreal root of $x^3 = 1.$  Compute
\[(1 - \omega + \omega^2)^4 + (1 + \omega - \omega^2)^4.\]
Question:
Let $\omega$ be a nonreal root of $x^3 = 1.$  Compute
\[(1 - \omega + \omega^2)^4 + (1 + \omega - \omega^2)^4.\]
Answer:
Let's think step by step.

user
-16
Let $\omega$ be a nonreal root of $x^3 = 1.$  Compute
\[(1 - \omega + \omega^2)^4 + (1 + \omega - \omega^2)^4.\]
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