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AP EAMCET20228 Jul 2022Morning ShiftMathematicsComplex NumberActual

( 1-i 1+i )²⁰²²+ ( 1+i 1-i )²⁰²¹=

Options

  1. A- i
  2. Bi
  3. Ci +1
  4. Di -1

Correct answer

D. i -1

Step-by-step solution

( 1-i 1+i )²⁰²²+ ( 1+i 1-i )²⁰²¹ aligned & = ( (1-i)^2 1+i^2 )²⁰²²+ ( (1+i)^2 1-i^2 )²⁰²¹ & = ( -2 i 2 )²⁰²²+ ( 2 i 2 )²⁰²¹=(-i)²⁰²²+(i)²⁰²¹ & =(i)²⁰²²+(i)²⁰²¹=(i)^ 4 505+2 +(i)^ 4 505+1 & =(i)^1+(i)^1=-1+i=i=1 aligned

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