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$\left(\frac{-1+i \sqrt{3}}{2}\right)^{20}+\left(\frac{-1-i \sqrt{3}}{2}\right)^{20}=$
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The correct answer is:
$-1$
$\begin{aligned} & \text { As } \frac{-1+i \sqrt{3}}{2}=\omega \text { and } \frac{-1-i \sqrt{3}}{2}=\omega^2 \\ & \therefore(\omega)^{20}+\left(\omega^2\right)^{20}=\omega^{18} \cdot \omega^2+\omega^{39} \cdot \omega=\omega^2+\omega=-1\end{aligned}$
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