Q62.Let C be the circle in the complex plane with centre z0 = 12 (1 + 3i) and radius r = 1. Let z1 = 1 + i and the complex number z2 be outside circle C such that |z1 −z0||z2 −z0| = 1 . If z0, z1 and z2 are collinear, then the smaller value of |z2|2 is equal to (1) 5 (2) 7 2 2 (3) 13 (4) 3 2 2
What This Question Tests
This question combines concepts of circles and collinearity in the complex plane, requiring calculations of distances and applying the condition for collinear points to find the value of an unknown complex number.
Concepts Tested
Formulas Used
|z - z₀| = r
z = z₀ + k(z₁ - z₀) for collinearity
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📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Geometric interpretation of complex numbers
- Year
- 2023
- Shift
- 12 Apr Shift 1
- Q Number
- Q62
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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