JEE Advanced 2013 Paper 2 Mathematics Q10

Mathematics

Problem

Paragraph for Questions 9 and 10 Let S=S1∩S2∩S3S=S_1\cap S_2\cap S_3, where S1={z∈C:∣z∣<4}S_1=\{z\in\mathbb C:|z|<4\}, S2={z∈C:Im⁡[z−1+3i1−3i]>0}S_2=\left\{z\in\mathbb C:\operatorname{Im}\left[\dfrac{z-1+\sqrt3 i}{1-\sqrt3 i}\right]>0\right\} and S3={z∈C:Re⁡z>0}S_3=\{z\in\mathbb C:\operatorname{Re}z>0\}. min⁡z∈S∣1−3i−z∣\displaystyle\min_{z\in S}|1-3i-z| =

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