Math Gold Medalist

Lor

2022 AMC 12B

Problem 11

Let $f(n) = \left( \frac{-1+i\sqrt{3}}{2} \right)^n + \left( \frac{-1-i\sqrt{3}}{2} \right)^n$, where $i = \sqrt{-1}$. What is $f(2022)$?

$\textbf{(A) }\ -2 \qquad \textbf{(B) }\ -1 \qquad \textbf{(C) }\ 0 \qquad \textbf{(D) }\ \sqrt{3} \qquad \textbf{(E) }\ 2$

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   Solution