Answer
See below.
Work Step by Step
$\overline{zw}=\overline{(a+bi)(c+di)}=\overline{ac-bd+(bc+ad)i}=ac-bd-(bc+ad)i$
$\overline{z}\overline{w}=\overline{(a+bi)}\overline{(c+di)}=(a-bi)(c-di)=ac-bd-(bc+ad)i$
Thus they are equal thus we showed what we had to.