<s>[INST] Compute $(1 - \omega + \omega^2)(1 + \omega - \omega^2)$ where $\omega^3 = 1$ If $\omega^3 = 1$ and $\omega \neq 1$, then compute $(1 - \omega + \omega^2)(1 + \omega - \omega^2)$
I'm pretty lost, I don't really know where to start.
Thanks
 [/INST] $$
\begin{align}
(1-\omega+\omega^2)(1+\omega-\omega^2)
&=1-\omega^2+2\omega^3-\omega^4\\
&=1-\omega^2+2-\omega\\
&=4-(1+\omega+\omega^2)\\
&=4
\end{align}
$$
The last step is true since $(1+\omega+\omega^2)\overbrace{(1-\omega)}^{\text{not $0$}}=1-\omega^3=0$.
</s>