Q82.If z2 + z + 1 = 0, z ∈C , then ∑15n=1 (zn + (−1)a zn1 ) 2
What This Question Tests
This question requires recognizing the roots of the given quadratic equation as cube roots of unity (ω and ω^2) and then applying their properties (ω^3=1, 1+ω+ω^2=0) to simplify the given summation.
Concepts Tested
Formulas Used
z^2+z+1=0 => z = ω or ω^2
1+ω+ω^2=0
ω^3=1
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📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Properties of Cube Roots of Unity
- Year
- 2022
- Shift
- 26 Jun Shift 2
- Q Number
- Q82
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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