,

โดยใช้สูตร $\left|z\right|^{2}=z\bar{z}$ จะได้ 

\begin{eqnarray*}
\left|z_{1}+\bar{z_{2}}\right|^{2} & = & 3^{2}\\
\left(z_{1}+\bar{z_{2}}\right)\left(\bar{z_{1}}+z_{2}\right) & = & 9\\
z_{1}\bar{z_{1}}+z_{1}z_{2}+\overline{z_{1}z_{2}}+z_{2}\bar{z_{2}} & = & 9\\
\left|z_{1}\right|^{2}+z_{1}z_{2}+\overline{z_{1}z_{2}}+\left|z_{2}\right|^{2} & = & 9\quad\cdots\left(1\right)
\end{eqnarray*}

และ

\begin{eqnarray*}
\left|\bar{z_{1}}-z_{2}\right|^{2} & = & 5^{2}\\
\left(\bar{z_{1}}-z_{2}\right)\left(z_{1}-\bar{z_{2}}\right) & = & 25\\
z_{1}\bar{z_{1}}-\overline{z_{1}z_{2}}-z_{1}z_{2}+z_{2}\bar{z_{2}} & = & 25\\
\left|z_{1}\right|^{2}-\overline{z_{1}z_{2}}-z_{1}z_{2}+\left|z_{2}\right|^{2} & = & 25\quad\cdots\left(2\right)
\end{eqnarray*}

,

$(1)-(2):$

\begin{eqnarray*}
2\left(z_{1}z_{2}+\overline{z_{1}z_{2}}\right) & = & -16\\
\left|z_{1}z_{2}+\overline{z_{1}z_{2}}\right| & = & 8
\end{eqnarray*}