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MHT CET202620 April 2026Evening ShiftMathematicsComplex NumberActual

If i = -1 then [i¹⁸ + ( 1 i )²⁵ ]^3 =

Options

  1. A4 + 4i
  2. B2 + 2i
  3. C4 - 4i
  4. D2 - 2i

Correct answer

D. 2 - 2i

Step-by-step solution

We know that i^4 = 1 and i^2 = -1 . Evaluating the first term: i¹⁸ = (i^4)^4 i^2 = 1 (-1) = -1 Evaluating the second term: ( 1 i )²⁵ = 1 i²⁵ = 1 (i^4)^6 i = 1 i = -i Substituting these values into the given expression: [i¹⁸ + ( 1 i )²⁵ ]^3 = (-1 - i)^3 = -(1 + i)^3 = -(1^3 + 3(1)^2(i) + 3(1)(i)^2 + i^3) = -(1 + 3i - 3 - i) = -(-2 + 2i) = 2 - 2i Answer: 2 - 2i

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