If $\mathrm{z}=\mathrm{x}+$ iy satisfies the condition $|\mathrm{z}+1|=1$, then $\mathrm{z}$ lies on the

If $\mathrm{z}=\mathrm{x}+$ iy satisfies the condition $|\mathrm{z}+1|=1$, then $\mathrm{z}$ lies on the
  1. parabola with vertex $(0,0)$
  2. circle with centre $(-1,0)$ and radius 1
  3. circle with centre $(1,0)$ and radius 1
  4. Y-axis

Solution

Let $\mathrm{z}=\mathrm{x}+$ iy and $|\mathrm{z}+1|=1$ $\begin{aligned} & \therefore|(\mathrm{x}+1)+\mathrm{iy}|=1 \\ & \therefore \sqrt{(\mathrm{x}+1)^2+\mathrm{y}^2}=1 \Rightarrow(\mathrm{x}+1)^2+\mathrm{y}^2=1 \end{aligned}$ This is an equation of a circle with centre $(-1,0)$ and radius 1 .

Asked in: MHT CET 2021 (23 Sep Shift 2)

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