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KCET2021MathematicsComplex Number

If ( 1+i 1-i )^ x =1 , then

Options

  1. Ax=4 n+1, n N
  2. Bx=2 n+1, n N
  3. Cx=2 n, n N
  4. Dx=4 n, n N

Correct answer

D. x=4 n, n N

Step-by-step solution

Given, ( 1+i 1-i )^ x =1 aligned & [ (1+i) (1-i) (1+i) (1+i) ]^ x =1 & [ 1+i²+2 i 1²-i² ]^ x =1 & [ 1-1+2 i 1+1 ]^ x =1 & i^ x =1 & 4 n, n N . aligned

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