JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let \(S_1=\{z \in C:|z| \leq 5\}\), \(S_2=\left\{z \in C: I m\left(\frac{z+1-\sqrt{3} i}{1-\sqrt{3} i}\right) \geq 0\right\}\) and \(\mathrm{S}_3=\{\mathrm{z} \in \mathrm{C}: \operatorname{Re}(\mathrm{z}) \geq 0\}\). Then the area of the region \(S_1 \cap S_2 \cap S_3\) is:
- A \(\frac{125 \pi}{6}\)
- B \(\frac{125 \pi}{24}\)
- C \(\frac{125 \pi}{4}\)
- D \(\frac{125 \pi}{12}\)
Answer & Solution
Correct Answer
(D) \(\frac{125 \pi}{12}\)
Step-by-step Solution
Detailed explanation
\( S_1: x^2+y^2 \leq 25 \) \( S_2: \operatorname{Im} \text { of } \frac{z+(1-\sqrt{3} i)}{(1-\sqrt{3} i)} \geq 0 \) \( \operatorname{Im} \text { of }\left(\frac{x+i y}{1-\sqrt{3} i}+1\right) \geq 0 \)…
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