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AP EAMCET202123 Aug 2021Morning ShiftMathematicsComplex NumberActual

( 8 +i 8 )^8 ( 8 -i 8 )^8 is equal to

Options

  1. Ai
  2. B-i
  3. C1
  4. D2

Correct answer

C. 1

Step-by-step solution

aligned & ( 8 +i 8 )^8 ( 8 -i 8 )^8 & = i^8 ( 8 -i 8 )^8 (-i)^8 ( 8 +i 8 )^8 & =+ ( 8 -i 8 )^8 ( 8 +i 8 )^8 & =+ (e^ -i / 8 )^8 (e^ i / 8 )^8 = & + e^ -i e^ i [ e^ i = +i ] & =+ -i +i & = +(-1) (-1) =+1 aligned

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