,

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

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

,

$(1)-(2):$

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