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Manipal MET2020MathematicsComplex Number

If (3-i)^2 2+i =A+i B , where A and B are real numbers, then A and B are equal to

Options

  1. AA=-4, B=2
  2. BA=2, B=-4
  3. CA=2, B=4
  4. DNone of these

Correct answer

B. A=2, B=-4

Step-by-step solution

Given equation is (3-i)^2 2+i =A+i B 9-1-6 i 2+i =A+i B 8-6 i 2+i =A+i B array cc & 2(4-3 i) 2+i 2-i 2-i =A+i B & 28-4 i-6 i-3] 4+1 =A+i B & 2[5-10 i] 5 =A+i B & 2-4 i=A+i B array On equating the real and imginary parts from both sides, we get A=2 and B=-4

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