City Zhautykov 2023 Grade 8 Problem 7

Complex $x$ satisfies $x ^ 2 + x + 1 = 0$. Find the value of $x^{2023}+ \frac{1}{x^{2023}}$.

Replace sorry in the template below with your solution. See Answer Bank for acceptible answer declarations. Mathlib version used by the checker is v4.29.0.

import Mathlib.Data.Complex.Basic

def answer : ℂ := sorry

theorem solution (x : ℂ) (h : x ^ 2 + x + 1 = 0) : x ^ 2023 + 1 / x ^ 2023 = answer := sorry

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