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KCET2017MathematicsApplication of Derivatives

If ( ( 1+i 1-i )^ m ), then the least positive integralvalue of ( m ) is

Options

  1. A( 02 )
  2. B( 13 )
  3. C( 04 )
  4. D( 11 )

Correct answer

C. ( 04 )

Step-by-step solution

Given that, ( 1+i 1-i )^ m =1 ( 1+i 1-i 1+i 1+i )^ m =1 ( (1+i)² 1-(i)² )^ m =1 ( 1-1+2 i 1+1 )^ m =1 ( 2 i 2 )^ m =1 i^ m =1 For m=1 , we have i=1 , but i 1 For m=2 , we have i²=-1=1 , but -1 1 For m=3 , we have i³=-i=1 , but -i 1 For m=4 , we have i⁴=1 Therefore, m=4

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