Chapter 3 - Polynomial and Rational Functions - 3.3 Zeros of Polynomial Functions - 3.3 Exercises - Page 338: 117

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Step 1. Let $c=a+bi$ and $d=m+ni$, we have $c+d=(a+m)+(b+n)i$ and $\overline {c+d}=(a+m)-(b+n)i$ Step 2. We have $\overline {c}=a-bi$ and $\overline {d}=m-ni$, thus $\overline {c}+\overline {d}=(a+m)-(b+n)i$ Step 3. Thus we have: $\overline {c+d}=\overline {c}+\overline {d}$