I wish to determine if the extension
1) $L = Q(e^{2πi/n})$ is normal over $Q$,
2) $K(a)$ is normal over $F_3(t)$ where $a$ is root in a splitting field of $x^3-t$
For 1) Is it like polynomial $x^n-1$ splits completely in $Q(e^{2πi/n})$?
For 2) Is the idea like $K(a)$ is an extension of degree 3 over $Q$ but if it is normal then it contains all roots of the polynomial which leads to a contradiction of the degree?