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Manipal MET2012MathematicsComplex Number

The complex number z=x+i y which satisfy the equation | z-5 i z+5 i |=1 , lie on

Options

  1. Athe x -axis
  2. Bthe straight line y=5
  3. Ca circle passing through the origin
  4. DNone of the above

Correct answer

A. the x -axis

Step-by-step solution

| z-5 i z+5 i |=1 |z-5 i|=|z+5 i| Using definition |z-z₁ |= |z-z₂ | gives Perpendicular bisector of z₁ and z₂ . Perpendicular bisector of points (0,5) and (0,-5) . wheh lies on y -axis.

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