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JEE Main2003MathematicsComplex NumberActual

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

Options

  1. Ax=2 n+1 , where n is any positive integer
  2. Bx=4 n , where n is any positive integer
  3. Cx=2 n , where n is any positive integer
  4. Dx=4 n+1 , where n is any positive integer

Correct answer

B. x=4 n , where n is any positive integer

Step-by-step solution

( 1+ i 1- i )^ x =1 [ (1+ i ) 1- i ^2 ]^ x =1 ( 1+ i ^2+2 i 1+1 )^ x =1 ( i )^ x =1 ; x =4 n ; n 1⁺

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