📘 complex numbers and calculus

1. Problem: Given complex numbers $z = 1 + i$ and $y = 1 - i\sqrt{3}$, and $U = \frac{z^3}{y^2}$ with $U = \frac{\sqrt{2}}{2}(\cos \frac{\pi}{12} + i \sin \frac{\pi}{12})$. \textbf