04-03-2025

Problem: Find all $z \in \mathbb{C} $ such that
  1. $z^3 = 1$.
  2. $\left( \frac{z - 1}{z + 1} \right)^2 = 2 \iota $.
  3. $z^2 = 24 \iota - 7$.
  4. $z^3 = \iota - 1$.
  5. $z^4 = -1$.