11. Solve the equation $z^2 + z + 1 = 0$ 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 $y \neq 0$.
Ans. $z = ( -\frac{1}{2}, \pm \frac{\sqrt{3}}{2})$
