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COMEDK202510 May 2025Morning ShiftMathematicsComplex NumberActual

If x-1 3+i + y-1 3-i =i then (y, x)=

Options

  1. A(-4,-6)
  2. B(-6,-4)
  3. C(-4,6)
  4. D(6,-4)

Correct answer

D. (6,-4)

Step-by-step solution

Given the equation x-1 3+i + y-1 3-i = i . Multiply the first term by 3-i 3-i and the second term by 3+i 3+i to rationalize the denominators: (x-1)(3-i) 9+1 + (y-1)(3+i) 9+1 = i 3x - xi - 3 + i 10 + 3y + yi - 3 - i 10 = i Combine the numerators: (3x - 3 + 3y - 3) + i(-x + 1 + y - 1) = 10i (3x + 3y - 6) + i(y - x) = 0 + 10i Equating the real and imaginary parts: Real part: 3x + 3y - 6 = 0 x + y = 2 Imaginary part: y - x = 10 Adding the two equations: (x + y) + (y - x) = 2 + 10 2y = 12 y = 6 Substituting y = 6 into x

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