x² - x + 1 = 0
x = -(-1) ± √(-1)² - 4(1)(1)
2(1)
x = 1 ± √1 - 4
2
x = 1 ± √-3
2
x = 1 ± i√3
2
x = 0.5 ± 0.5i√3
x⁹ = (0.5 + 0.5i√3)⁹
x⁹ = (0.5 + 0.5i√3)²(0.5 + 0.5i√3)²(0.5 + 0.5i√3)²(0.5 + 0.5i√3)²(0.5 + 0.5i√3)
x⁹ = (0.25 + 0.5i√3 - 0.75)(0.25 + 0.5i√3 - 0.75)(0.25 + 0.5i√3 - 0.75)(0.25 + 0.5i√3 - 0.75)(0.5 + 0.5i√3)
x⁹ = (-0.5 + 0.5i√3)(-0.5 + 0.5i√3)(-0.5 + 0.5i√3)(-0.5 + 0.5i√3)(0.5 + 0.5i√3)
x⁹ = (0.25 - 0.5i√3 - 0.75)(0.25 - 0.5i√3 - 0.75)(0.5 + 0.5i√3)
x⁹ = (-0.5 - 0.5i√3)(-0.5 - 0.5i√3)(0.5 + 0.5i√3)
x⁹ = (0.25 + 0.5i√3 - 0.75)(0.5 + 0.5i√3)
x⁹ = (-0.5 + 0.5i√3)(0.5 + 0.5i√3)
x⁹ = -0.25 - 0.5i√3 + 0.5i√3 - 0.75
x⁹ = -1
