Q62.If α, β ∈C are the distinct roots of the equation x2 −x + 1 = 0, then α101 + β107 is equal to (1) 2 (2) −1 (3) 0 (4) 1
What This Question Tests
This question assesses the knowledge of standard quadratic equations whose roots are related to complex cube roots of unity, and the ability to simplify high powers of these complex numbers using their fundamental properties.
Concepts Tested
Formulas Used
x^2 - x + 1 = 0 roots are -ω, -ω^2
ω^3 = 1
1 + ω + ω^2 = 0
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📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Properties of roots of unity
- Year
- 2018
- Shift
- 08 Apr
- Q Number
- Q62
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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