Question 11
Let $$
\begin{aligned} f(n) &= \left(\dfrac{-1 + i\sqrt3}{2}\right)^n \\ &\quad {}+ \left(\dfrac{-1 - i\sqrt3}{2}\right)^n, \end{aligned}
$$ where $i = \sqrt{-1}.$ What is $f(2022)?$
\begin{aligned} f(n) &= \left(\dfrac{-1 + i\sqrt3}{2}\right)^n \\ &\quad {}+ \left(\dfrac{-1 - i\sqrt3}{2}\right)^n, \end{aligned}
$$ where $i = \sqrt{-1}.$ What is $f(2022)?$