It's easy to embed the (cyclic) multiplicative group of a finite field into the multiplicative group of $\mathbb{C}$ (or other algebraically closed field of characteristic 0): assign to a generator of the finite cyclic group a corresponding primitive root of unity in $\mathbb{C}$. Though such embeddings are usually not unique, a fixed one is needed for example to define the Brauer character of a $p$-modular representation of a finite group.

More generally one can embed the multiplicative group $F^\times$ of an algebraic closure $F$ of $\mathbb{F}_p$ into $\mathbb{C}^\times$. This is somewhat less elementary and certainly less familiar. I'd be curious to know about the historical origin of such embeddings, but my immediate question is just a reference request:

What is a convenient modern reference for this larger type of embedding?

P.S. To clarify what I'm asking for, the *proof* of the embedding statement is not the issue (it requires some version of Zorn's Lemma, as does the original proof of existence of an algebraic closure of a finite field). I'd expect to find an explicit statement in some book, even in the form of a structured exercise, but it's not immediately obvious where to look. Occasionally some use is made in research papers of an embedding (without further comment).