The reason for me asking this question in the first place is that I need to find the Galois Group of Q(Zeta)/Q.
Now this would be incredibly easy if Q(Zeta) = Q(Zeta_12) as, because Zeta_12 is primitive this is just Z12*.
But I don't know if they are equal! :-s
If not, does anyone have any idea how to answer the question?
Many thanks. x