Solve the equation z2 + z + 1 = 0 for z = (x, y) by writing
(x, y) (x, y) + (x, y) + (1, 0) = (0, 0)
and then solving a pair of simultaneous equations in x and y.
Suggestion: Use the fact that no real number x satisfies the given equation to show that y ≠ 0.