import Mathlib

set_option maxHeartbeats 0

open BigOperators Real Nat Topology Rat

theorem amc12b_2021_p18
  (z : ℂ)
  (h₀ : 12 * Complex.normSq z = 2 * Complex.normSq (z + 2) + Complex.normSq (z^2 + 1) + 31) :
  z + 6 / z = -2 := by sorry