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MHT CET202615 April 2026Evening ShiftMathematicsComplex NumberActual

If is a complex cube root of unity, then the value of [ ( ¹⁰ + ²³) - 4 ] =

Options

  1. A- 3 2
  2. B- 1 2
  3. C1 2
  4. D3 2

Correct answer

C. 1 2

Step-by-step solution

Since is a complex cube root of unity, ^3 = 1 and 1 + + ^2 = 0 . ¹⁰ = ( ^3)^3 = ²³ = ( ^3)^7 ^2 = ^2 ¹⁰ + ²³ = + ^2 = -1 Substituting this into the given expression: [ ( ¹⁰ + ²³) - 4 ] = (- - 4 ) = (- 5 4 ) = - ( + 4 ) = - (- 4 ) = 1 2 Answer: 1 2

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