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NDA2023MathematicsComplex NumberActual

Consider equation-I: z^3+2 z^2+2 z+1=0 and equation -II: z¹⁹⁸⁵+z¹⁰⁰+1=0 Which of the following is a root of equation-I?

Options

  1. A– 1
  2. B– ω
  3. C- ^2
  4. Dω

Correct answer

D. ω

Step-by-step solution

Since, the given equation-II is z¹⁹⁸⁵+z¹⁰⁰+1=0 If z=-1,-1+1+1 0 If z=- , ¹⁹⁸⁵+ ¹⁰⁰+1 0 If z=- ^2, (- ^2 )¹⁹⁸⁵+ (- ^2 )¹⁰⁰+1 0 If z= , ¹⁹⁸⁵+ ¹⁰⁰+1=0 So option (D) is correct.

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