Let $K$ a subfield of $\mathbb{C}$. Show that $\mathbb{Q} \subset K$ Let $K$ a subfield of $\mathbb{C}$. Show that $\mathbb{Q} \subset K$.
To do this, I am trying to use an exercise done in class : Let $K$ a field, $\alpha \in K$ and $L$ a subfield of $K$. Then $L(\alpha)$ is the smallest subfield of $K$ containing $L$ and $\alpha$.
Is anyone could give me a hint to solve this problem?

By definition of a subfield, $K$ contains $0$ and $1$ and all finite sums of its elements and all negatives of its elements and all quotients (not by $0$) of its elements.
