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AP EAMCET2014MathematicsComplex Number

The least positive integer n for which (1+i)^n=(1-i)^n , is

Options

  1. A8
  2. B2
  3. C4
  4. D6

Correct answer

C. 4

Step-by-step solution

Given, (1+i)^n=(1-i)^n aligned & (1+i)^n (1-i)^n =1 & [ (1+i) (1+i) (1-i) (1+i) ]^n=1 & [ 1^2+i^2+2 i 1^2-i^2 ]^n=1 & [ 1-1+2 i 1+1 ]^n=1 & ( 2 i 2 )^n=1 & (i)^n=1 & n=4 & aligned

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