Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

have fun. it is a great topic

Answer 9

Thanks, signing off