# Tag Info

A cyclotomic field is a number field obtained by adjoining a complex primitive root of unity to $\mathbb Q$, the field of rational numbers.
$$\Phi_n(x) = \prod_\stackrel{1\le k\le n}{\gcd(k,n)=1} \left(x-e^{2i\pi\frac{k}{n}}\right)$$
$$[Q(ζ_n):Q]$$
is given by $φ(n)$ where $φ$ is Euler's phi function.