Sure, here is the translated text:

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II. (This question is worth 35 points) Let the set $Z=\left\{z_{1}\right.$, $\left.z_{2}, \cdots, z_{n}\right\}$ satisfy the inequality
$$
\min _{i \neq j}\left|z_{i}-z_{j}\right| \geqslant \max _{i}\left|z_{i}\right| \text {. }
$$

Find the largest $n$, and for this $n$, find all sets that satisfy the above condition.

Where the notation $\min (a, b, c)$ denotes the minimum of $a, b, c$, and $\max (a, b, c)$ denotes the maximum of $a, b, c$.
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Let $\left|z_{m}\right|=\max \left|z_{i}\right|$.
Thus, all points $z_{i}$ on the plane are distributed within a circle of radius $\left|z_{m}\right|=R$ centered at $z_{0}=0$.

It can be seen that on the circumference $R$, the six vertices $z,(j=1,2,3,4,5,6)$ of any inscribed regular hexagon, along with $z_{0}=0$, satisfy the given conditions for a total of 7 points.

If $n>7$, we prove that there must be two points $z^{\prime}, z^{\prime \prime}$ such that
$$
\left|z^{\prime}-z^{\prime \prime}\right|7$, then at least one of the sectors must contain two points $Z^{\prime}, Z^{\prime \prime}$. Without loss of generality, assume
$$
\left|z^{\prime}\right| \leqslant\left|z^{\prime \prime}\right|, \angle Z^{\prime} Z_{0} Z^{\prime \prime}=\varphi0$.