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MHT CET202620 April 2026Morning ShiftMathematicsComplex NumberActual

If w is a complex cube root of unity , then the value of w¹⁰ - w^7 + w^5 - w^2 + 1 is.

Options

  1. A0
  2. B-1
  3. C1
  4. Dw

Correct answer

C. 1

Step-by-step solution

Since w is a complex cube root of unity, w^3 = 1 and 1 + w + w^2 = 0 . Simplifying each term using w^3 = 1 : w¹⁰ = (w^3)^3 w = 1 w = w w^7 = (w^3)^2 w = 1 w = w w^5 = w^3 w^2 = 1 w^2 = w^2 Substituting these values into the given expression: w¹⁰ - w^7 + w^5 - w^2 + 1 = w - w + w^2 - w^2 + 1 = 0 + 0 + 1 = 1 Answer: 1

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