Automorphism Group of Complex Numbers over Real Numbers

Theorem
The field extension $\C / \R$ of complex numbers $\C$ over real numbers $\R$ has automorphism group $\operatorname{Aut}$:
 * $\operatorname{Aut} \paren {\C / \R} = \set {\operatorname{id}, \sigma}$

where:
 * $\operatorname{id}$ denotes the identity mapping
 * $\sigma$ denotes complex conjugation