Let $z, w \in \mathbb{C}$ each be a D1207: Complex number.

Denote $z = (a, b)$ and $w = (c, d)$. Using the definitions

(i)	D611: Complex multiplication operation
(ii)	D507: Complex conjugate

we have \begin{equation} \begin{split} \overline{z w} = \overline{(a, b) (c, d)} & = \overline{(a c - b d, a d + b c)} \\ & = (a c - b d, - a d -b c) \\ & = (a, -b)(c, -d) \\ & = \overline{(a, b)} \overline{(c, d)} \\ & = \overline{z} \, \overline{w} \end{split} \end{equation} $\square$