Homework Statement
Let ζ=e^((2*\pi*i)/7), E=Q(ζ), \xi=ζ + ζ^6.
Show that [Q(ζ):Q(\xi)]=2.
Find the generator of the galois group Gal(Q(ζ):Q(\xi)).
What is the minimal polynomial of \xi.
Homework Equations
The Attempt at a Solution
I know that [Q(ζ):Q]=6 and that Gal(Q(ζ):Q) is the cyclic...