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MHT CET202311 May 2023Evening ShiftMathematicsComplex NumberActual

If x= 5 1-2 i , i = -1 , then the value of x^3+x^2-x+22 is

Options

  1. A7
  2. B9
  3. C17
  4. D39

Correct answer

A. 7

Step-by-step solution

aligned & x= 5 1-2 i = 5(1+2 i ) 1+4 =1+2 i & x^2=(1+2 i )^2=1-4+4 i =-3+4 i & x^3=(-3+4 i )(1+2 i ) & =-3-6 i+4 i-8 & =-11-2 i & x^3+x^2-x+22 & =(-11-2 i )+(-3+4 i )-(1+2 i )+22 & =-11-2 i -3+4 i -1-2 i +22 & =7 & aligned

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