An algebra problem by Hobart Pao

Identify the correct statements regarding

$\left( \dfrac{-1 + i \sqrt{3}}{2} \right)^3$ and $\left( \dfrac{-1 - i \sqrt{3}}{2}\right)^6$

I. $\mathscr{Re}\left( \dfrac{-1 + i \sqrt{3}}{2} \right)^3 = \mathscr{Re}\left( \dfrac{-1 - i \sqrt{3}}{2}\right)^6$

II. $\mathscr{Im}\left( \dfrac{-1 + i \sqrt{3}}{2} \right)^ 3= \mathscr{Im}\left( \dfrac{-1 - i \sqrt{3}}{2}\right)^6$