# Math Help - Field extension question

1. ## Field extension question

I have this kind of problem in which I need help:

Let $S \subseteq \mathbb{C}$ be a subfield. Show that $S$ is the field extension of $\mathbb{Q}$, in other words, show that $\mathbb{Q} \subseteq S$.

Any help would be great.

2. Hint:

$1\in S$ implies $1+\ldots +1\in S$ , $-(1+\ldots+1)\in S$ and $0\neq x\in S\Rightarrow x^{-1}\in S$ .

Could you continue?