Chapter 3.5, Problem 16E

Assume that the nonzero complex numbers form a group $G$ with respect to multiplication. If $a$ and $b$ are real numbers and $i=\sqrt{-1}$, the conjugate of the complex number $a+bi$ is defined to be $a-bi$. With this notation, let $\varnothing :G\to G$ be defined by $\varnothing (a+bi)=a-bi$ for all $a+bi$ in $G$. Prove that $\varnothing$ is an automorphism of $G$.