Question 109, If the complex number $z$ satisfies $|z-\sqrt{3}|+|z+\sqrt{3}|=4$, then the maximum value of $|z+i|$ is

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(Here, the last sentence is a note to the translator, not part of the translation. The actual translation is above.)
Question 109, Solution: According to the conditions, point $\mathrm{z}$ is located on an ellipse with foci at $\pm \sqrt{3}$ and a semi-major axis of 2, and the semi-minor axis is 1, so $z=2 \cos \theta+i \cdot \sin \theta$. Therefore, we have:
$$
|z+i|=\sqrt{(2 \cos \theta)^{2}+(1+\sin \theta)^{2}}=\sqrt{-3\left(\sin \theta-\frac{1}{3}\right)+\frac{16}{3}} \leq \frac{4 \sqrt{3}}{3}
$$

Thus, the maximum value of $|z+i|$ is $\frac{4 \sqrt{3}}{3}$.