I'm not sure if my reasoning below is correct or not. If a=e^{[itex]\stackrel{\underline{2πi}}{5}[/itex]}, then Q(a) = {r + sa + ta^{2} + ua^{3} +va^{4} : r,s,t,u,v [itex]\in[/itex] Q} . [Is this correct?] Then [Q(a):Q] = 5 as {1, a, a^{2}, a^{3}, a^{4}} form a basis for Q(a) as a vector space over Q. However I am not sure if my reasoning above is correct as I have just seen a proof that [Q(a):Q] = 4 for the same a above. Thanks for your help.