If z^2 + z + 1 = 0, z ∈ C, then |Σ(z^n+(-1)^n 1/z^n)| is equal to_______.

Question

If z² + z + 1 = 0, z ∈ \(\mathbb{C}\), then \(|\sum\limits_{n=1}^{15}(z^n+(-1)^n\frac1{z^n})^2|\) is equal to_______.

Answer 1

Answer is 2

z² + z + 1 = 0

⇒ z = w, w²

 = |0 + 0 - 2| = 2