Example 5 (2002 National High School Competition Question) Given complex numbers $z_{1}, z_{2}$ satisfy $\left|z_{1}\right|=2,\left|z_{2}\right|=3$. If the angle between the vectors they correspond to is $60^{\circ}$, then $\left|\frac{z_{1}+z_{2}}{z_{1}-z_{2}}\right|=$ $\qquad$
Solve: Fill in $\frac{\sqrt{133}}{7}$. Reason: As shown in Figure $9-3$, by the cosine rule, we can get $\left|z_{1}+z_{2}\right|=\sqrt{19},\left|z_{1}-z_{2}\right|=\sqrt{7}$, hence $\left|\frac{z_{1}+z_{2}}{z_{1}-z_{2}}\right|=\frac{\sqrt{133}}{7}$.