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AP EAMCET2013MathematicsComplex Number

( 1+i 1-i )^4+ ( 1-i 1+i )^4 is equal to

Options

  1. A0
  2. B1
  3. C2
  4. D4

Correct answer

C. 2

Step-by-step solution

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

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