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 \(z + \frac{1}{z} + z^2 + \frac{1}{z^2}.\)
For the first problem, the minimum value is 32.
For the second problem, the answer is 5.
