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MHT CET202618 April 2026Morning ShiftMathematicsComplex NumberActual

The value of ( -1+i 3 2 )¹⁸ + ( -1-i 3 2 )¹⁸ is

Options

  1. A2
  2. B35
  3. C3
  4. D3 2

Correct answer

A. 2

Step-by-step solution

Let = -1+i 3 2 and ^2 = -1-i 3 2 be the complex cube roots of unity. The given expression can be written as ¹⁸ + ( ^2)¹⁸ . Since ^3 = 1 , we have ¹⁸ = ( ^3)^6 = 1^6 = 1 . Similarly, ( ^2)¹⁸ = ³⁶ = ( ^3)¹² = 1¹² = 1 . Therefore, the value of the expression is 1 + 1 = 2 . Answer: 2

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