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AP EAMCET2016MathematicsComplex Number

(1+i)²⁰¹⁶ (1-i)²⁰¹⁴ is equal to

Options

  1. A-2i
  2. B2i
  3. C2
  4. D-2

Correct answer

A. -2i

Step-by-step solution

We have, aligned & (1+i)²⁰¹⁶ (1-i)²⁰¹⁴ = [(1+i)^2 ]¹⁰⁰⁸ [(1-i)^2 ]¹⁰⁰⁷ = (1+2 i+i^2 )¹⁰⁰⁸ (1-2 i+i^2 )¹⁰⁰⁷ & = (2 i)¹⁰⁰⁸ (-2 i)¹⁰⁰⁷ = (2 i)¹⁰⁰⁸ (-1)¹⁰⁰⁷(2 i)¹⁰⁰⁷ & =-(2 i)¹⁰⁰⁸⁻¹⁰⁰⁷=-2 i aligned

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