Paragraph: Let $S=S_{1} \cap S_{2} \cap S_{3}$, where $S_{1}=\{z \in \mathbb{C}:|z|<4\}, \quad S_{2}=\left\{z \in \mathbb{C}: \operatorname{Im}\left[\frac{z-1+\sqrt{3} i}{1-\sqrt{3} i}\right]>0\right\}$ and $S_{3}=\{z \in \mathbb{C}: \operatorname{Re} z>0\}$.
Question: $\min _{z \in S}|1-3 i-\mathrm{z}|=$

• A

  $\frac{2-\sqrt{3}}{2}$
• B

  $\frac{2+\sqrt{3}}{2}$
• Correct answer
  C

  $\frac{3-\sqrt{3}}{2}$
• D

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

Hence, the correct answer is option: 'C'.