I am reading Dummit & Foote for studying undergraduate level field theory, and here is what I see on Page 555:
I followed the words of writers and understood the proof for a statement
$$\mathbb{Q}(\zeta_8) = \mathbb{Q}(i, \sqrt{2})$$
where $\zeta_8$ denotes the primitive 8th root of unity.
So here I am wondering whether we have a more generalized version of this statement for any arbitrary $\mathbb{Q}(\zeta_n)$, for example
$$\mathbb{Q}(\zeta_n) = \mathbb{Q}(i, ?)$$
where $\zeta_n$ denotes the primitive nth root of unity for some arbitrary $n \in \mathbb{N}$.
Can somebody tell me whether we really have this generalization? If so, which reference should I read to study it more deeply? Thanks!