find a basis for Q[e^(i*pi/3)]

Question

anonymous · Answer

the basis for this or for the basis for 
$$\mathbb Z[e^{\frac{\pi}{3}i}]$$?  i guess i am confused, because if i recall correctly if you are working over Q it would just be 1 and your root of unity

anonymous · Answer

sorry, over Q. 
I got {1, i*sqrt{3}}

anonymous · Answer

i think that looks good. you definitely need i and root 3, and you get both of those with your basis

anonymous · Answer

it has been a while, but your extension should be of degree 2, because 
$$\phi(3)=2$$ and you indeed have an extension of degree 2

anonymous · Answer

Thought that was right. just wasn't sure.  Thanks

anonymous · Answer

sorry i couldn't be more help. are you studying galois?

anonymous · Answer

Not yet. Not sure we get to that this semester, it may be next semester.

anonymous · Answer

have fun. it is a great topic

anonymous · Answer

Thanks, signing off