Let $\omega$ be a primitive 7th root of 1 over $\Bbb Q$ .Let $\alpha= \omega+\omega^6$. Find the minimum polynomial of $\alpha$ over $\Bbb Q$.
What I have so far is;
$\alpha - \omega = \omega^6$
$\alpha=1/\omega + \omega$
But I don't see how this is going to help as as I still don't have a root and can't figure our how to get the minimal polynomial when there is two variables.