Question 104, Given complex numbers $\mathrm{z}_{1}, \mathrm{z}_{2}$ satisfy the following conditions: $\left|\mathrm{z}_{1}\right|=2,\left|\mathrm{z}_{2}\right|=3,3 \mathrm{z}_{1}-2 \mathrm{z}_{2}=2-\mathrm{i}$, then $\mathrm{z}_{1} \mathrm{z}_{2}=$ $\qquad$ -
Question 104, Solution: According to the conditions: $z_{1} \cdot \overline{z_{1}}=4, z_{2} \cdot \overline{z_{2}}=9$, thus
$$
\begin{array}{l}
3 z_{1}-2 z_{2}=\frac{z_{1} \cdot z_{2} \overline{z_{2}}}{3}-\frac{z_{2} \cdot z_{1} \overline{z_{1}}}{2}=z_{1} z_{2} \cdot \frac{2 \bar{z}_{2}-3 \overline{z_{1}}}{6} \\
\Rightarrow z_{1} z_{2}=\frac{6\left(3 z_{1}-2 z_{2}\right)}{2 \overline{z_{2}}-3 \overline{z_{1}}}=\frac{6(2-i)}{-(2+i)}=-\frac{18}{5}+\frac{24}{5} i
\end{array}
$$

Therefore, the required $z_{1} z_{2}=-\frac{18}{5}+\frac{24}{5} i$.