MathematicsHard53×since 2002Q3204Let S1={z∈C:∣z∣≤5},S2={z∈C:Im(z+1−3i1−3i)≥0}S_1=\{z \in \mathbf{C}:|z| \leq 5\}, S_2=\left\{z \in \mathbf{C}: \operatorname{Im}\left(\frac{z+1-\sqrt{3} i}{1-\sqrt{3} i}\right) \geq 0\right\}S1={z∈C:∣z∣≤5},S2={z∈C:Im(1−3iz+1−3i)≥0} and S3={z∈C:Re(z)≥0}S_3=\{z \in \mathbf{C}: \operatorname{Re}(z) \geq 0\}S3={z∈C:Re(z)≥0}. Then the area of the region S1∩S2∩S3S_1 \cap S_2 \cap S_3S1∩S2∩S3 is :A125π24\frac{125 \pi}{24}24125πB125π6\frac{125 \pi}{6}6125πC125π12\frac{125 \pi}{12}12125πD125π4\frac{125 \pi}{4}4125πCheck answerSkip