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AP EAMCET20226 Jul 2022Evening ShiftMathematicsComplex NumberActual

If ₁, ₂, , ₂₃ are the 23 rd roots of unity, then ₁⁴⁷+ ₂⁴⁷+ .+ ₂₃⁴⁷=

Options

  1. A23
  2. B-1
  3. C1
  4. D0

Correct answer

D. 0

Step-by-step solution

₁, ₂, ₃, , ₂₃ are the 23 rd roots of unity. ²³-1=0 ²³=1 Now, ₁⁴⁷+ ₂⁴⁷+ + ₂₃⁴⁷ aligned & = ₁ ( ₁²³ )^2+ ₂ ( ₂²³ )^2+ + ₂₃ ( ₂₃²³ )^2 & = ₁+ ₂+ + ₂₃ aligned Sum of roots =0

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