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KCET2018MathematicsComplex Number

If ( ( 1-i 1+i )⁹⁶=a+i b ) then ( (a, b) ) is

Options

  1. A( (1,1) )
  2. B( (1,0) )
  3. C( (0,1) )
  4. D( (0,-1) )

Correct answer

B. ( (1,0) )

Step-by-step solution

Given that, ( ( 1-i 1+i )⁹⁶=a+i b ) Now, ( 1-i 1+i = 1-i 1+i 1-i 1-i =-i ) So, ( i⁹⁶=a+i b ) ( (i⁴ )²⁴=a+i b ) ( 1+i(0)=a+i b ) Therefore, ( (a, b) ) is ( (1,0) ).

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