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
- A the \(\mathrm{Y}\) - axis
- B a parabola
- C a hyperbola
- D the X-axis
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 \\ &…
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