4. $\left|z_{1}+z_{2}\right|=4 \cdot \mid z_{1}-z_{2}=3 . z_{1}, z_{2} \in \mathbb{C}$. Find the range of $\left|z_{1}, z_{2}\right|$

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4. $\left|z_{1}+z_{2}\right|=4 \cdot \mid z_{1}-z_{2}=3 . z_{1}, z_{2} \in \mathbb{C}$. Find the range of $\left|z_{1}, z_{2}\right|$
$$
\begin{array}{l}
\text { 4. }\left[\frac{7}{4}, \frac{25}{4}\right] \\
\left|z_{1} \cdot z_{2}\right| \\
=\left|\frac{\left(z_{1}+z_{2}\right)+\left(z_{1}-z_{2}\right)}{2}\right| \cdot\left|\frac{\left(z_{1}+z_{2}\right)-\left(z_{1}-z_{2}\right)}{2}\right| \\
=\frac{1}{4}\left|\left(z_{1}+z_{2}\right)^{2}-\left(z_{1}-z_{2}\right)^{2}\right| \\
\text { Also, }\left|z_{1}+z_{2}\right|=4,\left|z_{1}-z_{2}\right|=3,
\end{array}
$$

It is known that the maximum value is $\frac{1}{4}\left(4^{2}+3^{2}\right)=\frac{25}{4}$, and the minimum value is $\frac{1}{4}\left(4^{2}-3^{2}\right) \div \frac{7}{4}$.