Solution (source code)

= Solution

Write $z=re^{i\theta}$ with $-\pi<\theta\leq\pi$. Its principal sixth root is $r^{1/6}e^{i\theta/6}$, whose <complex argument> lies in $(-\pi/6,\pi/6]$. Equality with $2e^{i\pi/6}$ forces $r=64$ and $\theta=\pi$, so \b[$z=-64$].