Fix an algebraic closure $\overline{\mathbf{Q}}$ of the rational numbers.
Let $\mathbf{Q}\subset K$ be a number field.
I know that the degree $[K:\mathbf{Q} ]$ equals the number of embeddings of $K$ into the complex numbers.
Does $[K:\mathbf{Q}]$ also equal to the number of embeddings of $K$ into $\overline{\mathbf{Q}}$?