Answer
See explanations.
Work Step by Step
Step 1. Let $c=a+bi$ and $d=m+ni$, we have $c\cdot d=(a+bi)(m+ni)=(am-bn)+(an+bm)i$ and $\overline {c\cdot d}=(am-bn)-(an+bm)i$
Step 2. We have $\overline {c}=a-bi$ and $\overline {d}=m-ni$, thus $\overline {c}\cdot\overline {d}=(a-bi)(m-ni)=(am-bn)-(an+bm)i$
Step 3. Thus we have: $\overline {c\cdot d}=\overline {c}\cdot\overline {d}$
