Q81.Let z1, z2 be the roots of the equation z2 + az + 12 = 0 and z1, z2 form an equilateral triangle with origin. Then, the value of |a| is
What This Question Tests
This question combines the concepts of roots of a quadratic equation with the geometric condition for three complex numbers (including the origin) to form an equilateral triangle, requiring algebraic manipulation of complex numbers.
Concepts Tested
Formulas Used
z₁² + z₂² + z₁z₂ = 0 (for origin, z₁, z₂ forming equilateral triangle)
z₁ + z₂ = -a
z₁z₂ = 12
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📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Geometric Properties of Complex Numbers
- Year
- 2021
- Shift
- 18 Mar Shift 1
- Q Number
- Q81
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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