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AP EAMCET202125 Aug 2021Morning ShiftMathematicsComplex NumberActual

If n is a positive integer, then (1+i 3 )^n+(1-i 3 )^n is equal to

Options

  1. A2^ n-1 n 3
  2. B2^n n 3
  3. C2^ n+1 n 3
  4. D2^ 2 n n 3

Correct answer

C. 2^ n+1 n 3

Step-by-step solution

We have, aligned & (1+ 3 i)^n-(1- 3 i)^n & =2^n [ ( 3 +2 3 )^n+ ( 3 -i 3 )^n ] & [ 1 3 i=2 ( 3 i 3 ) ] & =2^n [ n 3 +i n 3 + n 3 -i n 3 ] & =2^ n+1 n 3 aligned

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