Q19.Let the curve z(1 + i) + ¯z(1 −i) = 4, z ∈C, divide the region |z −3| ≤1 into two parts of areas α and β . Then |α −β| equals : (1) 1 + π2 (2) 1 + π3 (3) 1 + π6 (4) 1 + π4
What This Question Tests
This question requires interpreting complex number equations geometrically as a line and a circle, then finding the areas of the two parts into which the circle's region is divided by the line.
Concepts Tested
Formulas Used
z + z̄ = 2Re(z)
z - z̄ = 2iIm(z)
Area of circle = πr²
Area of a circular segment
📚 NCERT Sections This Tests
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📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Geometric interpretation of complex numbers and area of regions
- Year
- 2025
- Shift
- 22 Jan Shift 2
- Q Number
- Q19
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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