Prove that \( \left(\frac{-1+i \sqrt{3}}{2}\right)^{n}+\left(\frac{...

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Prove that \( \left(\frac{-1+i \sqrt{3}}{2}\right)^{n}+\left(\frac{-1-i \sqrt{3}}{2}\right)^{n} \) is equal to \( -1 \) if \( n \) is not a multiple of 3.
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