Q62.If 𝛼 and 𝛽 be the roots of the equation 𝑥2 - 2𝑥+ 2 = 0, then the least value of 𝑛 for which 𝛼 𝑛= 1 is 𝛽 (1) 5 (2) 4 (3) 2 (4) 3
What This Question Tests
This question tests the ability to find the complex roots of a quadratic equation, convert them to polar form, and then apply De Moivre's theorem to determine the least integer 'n' that satisfies the given condition.
Concepts Tested
Formulas Used
x = (-b ± sqrt(b²-4ac))/(2a)
z = r(cosθ + isinθ)
(cosθ + isinθ)^n = cos(nθ) + isin(nθ)
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📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Roots of a quadratic equation and De Moivre's Theorem
- Year
- 2019
- Shift
- 08 Apr Shift 1
- Q Number
- Q62
- Type
- MCQ
- NCERT Ref
- Class 11 Maths Ch 5: Complex Numbers and Quadratic Equations
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