Q61.Let 𝛼 and 𝛽 be the roots of the equation 𝑥2 + 2𝑥+ 2 = 0, then 𝛼15 + 𝛽15 is equal to (1) -512 (2) 128 (3) 512 (4) -256
What This Question Tests
This question requires finding the complex roots of a quadratic equation, expressing them in polar form, and then using De Moivre's theorem to calculate high powers of these roots.
Concepts Tested
Formulas Used
x = r(cosθ + i sinθ)
(cosθ + i sinθ)^n = cos(nθ) + i sin(nθ)
📚 NCERT Sections This Tests
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Chemistry Class 11 · Chapter 1
1.27 If the solubility product of CuS is 6 × 10–16, calculate the maximum molarity of CuS in aqueous solution.
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Physics Class 11 · Chapter 2
2.2 A regular hexagon of side 10 cm has a charge 5 mC at each of its vertices. Calculate the potential at the centre of the hexagon.
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5.15 Discuss the nature of bonding in the following coordination entities on the basis of valence bond theory: (i) [Fe(CN)6] 4– (ii) [FeF6] 3– (iii) [Co(C2O4)3]3– (iv) [CoF6] 3–
📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Powers of complex roots
- Year
- 2019
- Shift
- 09 Jan Shift 1
- Q Number
- Q61
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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