Let $a,$ $b,$ $c$ be distinct integers, and let $\omega$ be a complex number such that $\omega^3 = 1$ and $\omega \neq 1.$ Find the smallest possible value of \[|a + b \omega + c \omega^2|.\]
You get the minimum value when a = -2, b = 0, and c = 2. Then |a + bw + cw^2| = 2*sqrt(3).
