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AP EAMCET2006MathematicsComplex Number

The locus of the point z=x+i y satisfying the equation | z-1 z+1 |=1 is given by :

Options

  1. Ax=0
  2. By=0
  3. Cx=y
  4. Dx+y=0

Correct answer

A. x=0

Step-by-step solution

| z-1 z+1 |=1 | x+i y-1 x+i y+1 |=1 |(x-1)+i y|=|(x+1)+i y| (x-1)^2+y^2 = (x+1)^2+y^2 x^2-2 x+1+y^2=x^2+1+2 x+y^2 4 x=0 x=0

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