Let $\displaystyle w = \frac {-1}{2} + \frac {3^{1/2}}{2}i$

Find the minimum polynomial for w over Q.

I know that the minimum poly is the monic function f such that f(w) = 0.

Nevermind, guys, I finally got the answer, is it p(x) = x^2 + x + 1?

It looks so easy now, but it took me so long to get it. Thanks.