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BITSAT2014MathematicsComplex NumberActual

The complex number z=z+i y which satisfies the equation | z-3 i z+3 i |=1, lies on

Options

  1. Athe X -axis
  2. Bthe straight line y=3
  3. Ca circle passing through origin
  4. DNone of the above

Correct answer

A. the X -axis

Step-by-step solution

| z-3 i z+3 i |=1 |z-3 i|=|z+3 i| [if |z-z₁ |= |z+z₂ |, then it is a perpendicular bisector of z₁ and z₂ ] Hence, perpendicular bisector of (0,3) and (0,-3) is X -axis.

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