Theorem CRSM Conjugation Respects Vector Scalar Multiplication

Suppose $\vect{x}$ is a vector from $\complex{m}$, and $\alpha\in\complexes$ is a scalar. Then \begin{equation*} \conjugate{\alpha\vect{x}}=\conjugate{\alpha}\,\conjugate{\vect{x}} \end{equation*}

Proof
(in context)