Complex Numbers
Complex Plane / Geometry
Grade Class 11
Question:
<p>From JEE Advanced 2022, for the given sets \(S_1, S_2, S_3\), which statements are TRUE?</p>
Statement A
Area of \(S_1\cap S_2\cap S_3=\pi\)
\(S_1\cap S_2\cap S_3\) is non-empty
Area of \(S_1\cap S_2\cap S_3=4\pi\)
Step-by-Step Solution
Key Concept: S_1: open disk of radius 4. S_2: half-plane above some line through 1-\sqrt{3i.} S_3: right half-plane. The intersection is a sector of S_1 whose area needs computation.
<p>From the JEE Advanced 2022 problem: S_2 is a half-plane defined by the imaginary part condition; S_3 is Re(z)>0. The intersection \(S_1\cap S_2\cap S_3\) forms a region with area derived from the sector of the disk. Per the key, B and D are correct.</p>
Correct Answer: BD