Hi I really need help in how to determine sub fields $L$ of $\mathbb{C}$ over $\mathbb{Q}$ and finding $[L:\mathbb{Q}]$. The question is:
Find subfields $L$ of $\mathbb{C}$ that are splitting fields over $\mathbb{Q}$, find $[L:\mathbb{Q}]$
$\begin{array}{ll} \mathrm{(i)} & t^8 + 1 \\ \mathrm{(ii)} & t^4 -4t^2 +1\\ \mathrm{(iii)} & t^3 -5\\ \mathrm{(iv)} & t^{17} - 1\\ \end{array}$
Any help would be great!