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

The equation |z-i|=|z-1|,i=-1, represents:
  1. a circle of radius 12
  2. a circle of radius 1
  3. the line through the origin with slope 1
  4. the line through the origin with slope -1

Solution

Let z=x+iy

z-i=z-1⇒x2+(y-1)2=(x-1)2+y2

⇒y=x
Hence, the equation represents a line through the origin with slope 1 .

Asked in: JEE Main 2019 (12 Apr Shift 1)

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