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AP EAMCET202318 May 2023Evening ShiftMathematicsComplex NumberActual

In the Argand plane, the values of Z satisfying the equation | z -1|=| i ( z +1)| lie on

Options

  1. Athe Y - axis
  2. Ba parabola
  3. Ca hyperbola
  4. Dthe X-axis

Correct answer

A. the Y - axis

Step-by-step solution

aligned & | z -1|=| i ( z +1)| & | z -1|=| i | | z +1| & | z -1|^2=| z +1|^2 & | x + iy -1|^2=| x + iy +1|^2 & ( x -1)^2+ y ^2=( x +1)^2+ y ^2 & x ^2+1-2 x = x ^2+1+2 x & 4 x =0 x =0 aligned which is equation of the y -axis.

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