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AP EAMCET202017 Sep 2020Morning ShiftMathematicsComplex NumberActual

If (2 =-1-i 3 ) and (2 =-1+i 3 ), then (5 ^4+5 ^4+7 ⁻¹ ⁻¹ ) is equal to

Options

  1. A-1
  2. B-2
  3. C0
  4. D2

Correct answer

D. 2

Step-by-step solution

(2 =-1-i 3 , 2 =-1+i 3 ) ( (5 ^4+5 ^4+7 ⁻¹ ⁻¹ ) ) ( aligned & =5 ( ^4+ ^4 )+ 7 & =5 [ ( ^2+ ^2 )^2-2 ^2 ^2 ]+ 7 & =5 [ 1 4 (2 +2 )^2-2 ^2-2 ^2 ^2 ]+ 7 & =5 [ ( 1 4 4-2 )^2-2 ]+7=5[1-2]+7=2 aligned )

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