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AP EAMCET · Maths · Complex Number

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

  1. A the \(\mathrm{Y}\) - axis
  2. B a parabola
  3. C a hyperbola
  4. D the X-axis
Verified Solution

Answer & Solution

Correct Answer

(A) the \(\mathrm{Y}\) - axis

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { }|\mathrm{z}-1|=|\mathrm{i}(\mathrm{z}+1)| \\ & \Rightarrow|\mathrm{z}-1|=|\mathrm{i}| \cdot|\mathrm{z}+1| \\ & \Rightarrow|\mathrm{z}-1|^2=|\mathrm{z}+1|^2 \\ & \Rightarrow|\mathrm{x}+\mathrm{iy}-1|^2=|\mathrm{x}+\mathrm{iy}+1|^2 \\ &…