Solution
= Solution
The number being squared has <polar form of a complex number> $e^{2\pi i/3}$. Squaring doubles its argument, giving $e^{4\pi i/3}=-1/2-i\sqrt3/2$. Hence
$$
\boxed{\Re z=-\frac12,\qquad\Im z=-\frac{\sqrt3}{2}.}
$$
= Solution
The number being squared has <polar form of a complex number> $e^{2\pi i/3}$. Squaring doubles its argument, giving $e^{4\pi i/3}=-1/2-i\sqrt3/2$. Hence
$$
\boxed{\Re z=-\frac12,\qquad\Im z=-\frac{\sqrt3}{2}.}
$$