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The locus of a point z represented by the equation z - 1 = | z - i | on the argand plane is (where, z ∈ C , i = - 1 )

Options

  1. Aa circle of radius 1
  2. Ban ellipse with foci at 1 and – i
  3. Ca line passing through the origin
  4. Da circle on the line joining 1 and – i as diameter

Correct answer

C. a line passing through the origin

Step-by-step solution

Given, z - 1 = z - i ⇒ z lies on the perpendicular bisector of the line joining ( 1 , 0 ) and ( 0 , 1 ) and it is a straight line passing through the origin.

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