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AP EAMCET202119 Aug 2021Evening ShiftMathematicsComplex NumberActual

If | z - 2 | = | z - 1 | , where z is a complex number, then locus of z is a straight line

Options

  1. A Parallel to  x −  axis 
  2. B Parallel to  y −  axis 
  3. C Parallel to  y = x
  4. D Parallel to  y = - x

Correct answer

B.  Parallel to  y −  axis 

Step-by-step solution

Given | z - 2 | = | z - 1 | On squaring both sides, we get z - 2 z ¯ - 2 = z - 1 z ¯ - 1 ⇒ z z ¯ - 2 z ¯ - 2 z + 4 = z z ¯ - z ¯ - z + 1 ⇒ z ¯ + z = 3 Now, putting z = x + i y , we get x + i y + x - i y = 3 ⇒ x = 3 2 Hence, locus of z is a straight line parallel to y - axis

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