Q82.Let z = 1−i√32 , i = √−1. Then the value of 21 + (z + 1z ) 3 + (z2 + z21 ) 3 + (z3 + z31 ) 3 + … + (z21 + z211 ) 3 is______.
What This Question Tests
This problem involves recognizing a complex number as a cube root of unity, using its properties (especially z + 1/z), and summing a series of cubic terms based on powers of this complex number.
Concepts Tested
Formulas Used
ω = e^(i2π/3)
ω^2 = e^(i4π/3)
z + 1/z = 2 Re(z)
ω + ω^2 + 1 = 0
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📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Cube roots of unity
- Year
- 2021
- Shift
- 26 Aug Shift 1
- Q Number
- Q82
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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