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AP EAMCET202021 Sep 2020Morning ShiftMathematicsComplex NumberActual

((-i+ 3 )³⁰⁰+(-i- 3 )³⁰⁰= )

Options

  1. A(2³⁰⁰ )
  2. B(2³⁰¹ )
  3. C(2¹⁰⁰ )
  4. D(-2³⁰⁰ )

Correct answer

B. (2³⁰¹ )

Step-by-step solution

( aligned &(-i+ 3 )³⁰⁰+(-i- 3 )³⁰⁰=(i- 3 )³⁰⁰ +(-i- 3 )³⁰⁰ &= i³⁰⁰(1+i 3 )³⁰⁰+i³⁰⁰(-1+i 3 )³⁰⁰ &= (-2 w^2 )³⁰⁰+(2 w)³⁰⁰ where w is cube root of unity &= 2³⁰⁰ [ (w^2 )³⁰⁰+w³⁰⁰ ]=2³⁰⁰ 2=2³⁰¹ aligned ) Hence, option (b) is correct.

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