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COMEDK20269 May 2026Morning ShiftMathematicsComplex NumberActual

The conjugate of z = (4 + i)(1 - i) (1 + i)(2 - i)

Options

  1. A1 2 + 1 2 i
  2. B6 5 + 7 5 i
  3. C6 5 - 7 5 i
  4. D1 2 - 1 2 i

Correct answer

B. 6 5 + 7 5 i

Step-by-step solution

z = (4 + i)(1 - i) (1 + i)(2 - i) Simplifying the numerator and denominator: (4 + i)(1 - i) = 4 - 4i + i - i^2 = 5 - 3i (1 + i)(2 - i) = 2 - i + 2i - i^2 = 3 + i Substituting these values: z = 5 - 3i 3 + i Multiplying the numerator and denominator by the conjugate of the denominator: z = 5 - 3i 3 + i 3 - i 3 - i z = 15 - 5i - 9i + 3i^2 3^2 - i^2 z = 15 - 14i - 3 9 + 1 z = 12 - 14i 10 = 6 5 - 7 5 i The conjugate of z is: z = 6 5 + 7 5 i Answer: 6 5 + 7 5 i

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