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AP EAMCET2011MathematicsComplex Number

(1+i)²⁰¹¹ (1-i)²⁰⁰⁹ is equal to

Options

  1. A-1
  2. B1
  3. C2
  4. D-2

Correct answer

D. -2

Step-by-step solution

aligned & (1+i)²⁰¹¹ (1-i)²⁰⁰⁹ = ( 2 )²⁰¹¹ ( 1 2 + i 2 )²⁰¹¹ ( 2 )²⁰⁰⁹ ( 1 2 - i 2 )²⁰⁰⁹ & = ( 2 )^2 (e^ i 4 )²⁰¹¹ (e^ - i 4 )²⁰⁰⁹ =2 (e^ i 4 )⁴⁰²⁰ & =2 (e^ i )¹⁰⁰⁵=2(-1)¹⁰⁰⁵=-2 aligned

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