A colleague asks me the following: "I wonder if you can give me a reference - or a guidance where to look – from a fact I recall from graduate school. I’m sure it can be generalized quite a bit but in the simplest form is it is the 'double density theorem':

Let $F$ be a number field and $j_1$ and $j_2$ two embeddings of $F$ into the complex plane $\mathbb C$ which are NOT related by complex conjugation: i.e. $j_2$ is not equal $\bar{j_1}$. Then then map $$ j_1 \times j_2 : F \to \mathbb C \times\mathbb C $$ has a dense image ( in the usual metric topology)."