I'm not sure if my reasoning below is correct or not.
If a=e\stackrel{\underline{2πi}}{5}, then Q(a) = {r + sa + ta2 + ua3 +va4 : r,s,t,u,v \in Q} . [Is this correct?]
Then [Q(a):Q] = 5 as {1, a, a2, a3, a4} form a basis for Q(a) as a vector space over Q.
However I am not sure if my...