Question 52
Find all complex numbers $z$ such that
$$ \mathrm{Re}(z) = 9 \quad \text{and} \quad \mathrm{Im}(z^2) = \mathrm{Im}(z^3). \qquad (\text{AIME 2007}) $$
$$ \mathrm{Re}(z) = 9 \quad \text{and} \quad \mathrm{Im}(z^2) = \mathrm{Im}(z^3). \qquad (\text{AIME 2007}) $$