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JEE Main201912 Apr 2019Morning ShiftMathematicsComplex NumberActual

The equation | z - i | = | z - 1 | , i = - 1 , represents:

Options

  1. Aa circle of radius 1 2
  2. Ba circle of radius 1
  3. Cthe line through the origin with slope 1
  4. Dthe line through the origin with slope - 1

Correct answer

C. the line through the origin with slope 1

Step-by-step solution

Let z = x + i y z - i = z - 1 ⇒ x 2 + ( y - 1 ) 2 = ( x - 1 ) 2 + y 2 ⇒ y = x Hence, the equation represents a line through the origin with slope 1 .

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