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MHT CET202210 Aug 2022Morning ShiftMathematicsComplex NumberActual

If ( 1-i 1+i )¹⁰⁰=a+i b , where, a b R and i= -1 , then (a, b) is equal to

Options

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

Correct answer

A. (1,0)

Step-by-step solution

aligned & ( 1-i 1+i )¹⁰⁰= (1-i)(1-i) (1+i)(1-i) ¹⁰⁰= ( 1-1-2 i 1+1 )¹⁰⁰=(-i)¹⁰⁰=1=a+i b & a=1 and b=0 aligned

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