Example 2. Let $p \neq 0$, and the quadratic equation with real coefficients $z^{2}-2 p z+q=0$ has imaginary roots $z_{1}$ and $z_{2}$. The corresponding points of $z_{1}$ and $z_{2}$ in the complex plane are $Z_{1}$ and $Z_{2}$. Find the length of the major axis of the ellipse with foci at $Z_{1}$ and $Z_{2}$ and passing through the origin. (84 National College Entrance Examination)