I'm not sure if my reasoning below is correct or not.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Degree of fields query

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