Let , where S_1 = z C : |z| 0 and S_3 = z C : Re z > 0 . equals…

MATHEMATICS · Single correct · CBSE · Mathematics · Complex Numbers and Quadratic Equations · Complex Numbers and Quadratic Equations

Problem

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[ \frac{z - 1 + \sqrt{3}i}{1 - \sqrt{3}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∣\min_{z \in S} |1 - 3i - z| equals to (1) 2−32\frac{2 - \sqrt{3}}{2} (2) 2+32\frac{2 + \sqrt{3}}{2} (3) 3−32\frac{3 - \sqrt{3}}{2} (4) 3+32\frac{3 + \sqrt{3}}{2}

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