Mathematics

Problem

Let

S = S_1 \cap S_2 \cap S_3

, where

S_1 = \{z \in \mathbb{C} : |z| < 4\},

S_2 = \left\{ z \in \mathbb{C} : \operatorname{Im}\left[ \frac{z - 1 + \sqrt{3}i}{1 - \sqrt{3}i} \right] > 0 \right\}

and

S_3 = \{z \in \mathbb{C} : \operatorname{Re} z > 0\}.

\min_{z \in S} |1 - 3i - z|

equals to a.

\frac{2 - \sqrt{3}}{2}

\frac{2 + \sqrt{3}}{2}

\frac{3 - \sqrt{3}}{2}

\frac{3 + \sqrt{3}}{2}