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JEE Main202226 Jul 2022Evening ShiftMathematicsComplex NumberActual

If z = x + i y satisfies z - 2 = 0 and z - i - z + 5 i = 0 , then

Options

  1. Ax + 2 y - 4 = 0
  2. Bx 2 + y - 4 = 0
  3. Cx + 2 y + 4 = 0
  4. Dx 2 - y + 3 = 0

Correct answer

C. x + 2 y + 4 = 0

Step-by-step solution

Given, z = x + i y Also, z = 2 So, x 2 + y 2 = 4           . . . 1 Now, z - i = z + 5 i ⇒ z - i 2 = z + 5 i 2 ⇒ x 2 + y - 1 2 = x 2 + y + 5 2 ⇒ y = - 2           . . . 2 So, x = 0 by solving equation 1   &   2 Hence, only x + 2 y + 4 = 0 is true, as point only satisfy this equation.

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