Q61.Let A = {z ∈C : z−1z+1 < 1} and B = {z ∈C : arg( z+1z−1 ) = 2π3 }. Then A ∩B is (1) a portion of a circle centred at (0, −1√3 ) that (2) a portion of a circle centred at (0, −1√3 ) that lies in the second and third quadrants only lies in the second quadrant only (3) an empty set (4) a portion of a circle of radius 2 that lies in the √3 third quadrant only
What This Question Tests
This question requires interpreting the geometric loci defined by the modulus and argument conditions for complex numbers, identifying them as a circle/region and a circular arc respectively, then finding their intersection.
Concepts Tested
Formulas Used
|z-z₁| < r
arg((z-z₁)/(z-z₂)) = θ
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📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Geometric interpretation of complex numbers
- Year
- 2022
- Shift
- 26 Jun Shift 1
- Q Number
- Q61
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers
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