Exam question: Showing $z = \left(\frac{1 +z}{\left|1 + z\right|} \right)^2$ for $z\in\mathbb{C}$ and $\left| z \right| = 1$
Suppose $z \neq -1$ is a complex number of norm 1. Prove that $(\frac{1+z}{|1+z|})^2 =z $