Let z be a complex number such that |z - 5 - i| = 5. Find the minimum value of \(|z - 1 + 2i|^2 + |z - 9 - 4i|^2\).

Let z be a complex number such that z^5 = 1 and \(z \neq 1\). Compute \(z + \frac{1}{z} + z^2 + \frac{1}{z^2}.\)

Guest Apr 18, 2019