If the complex number $\mathrm{z}=x+\mathrm{i} y$, where $\mathrm{i}=\sqrt{-1}$, satisfies the condition…

If the complex number $\mathrm{z}=x+\mathrm{i} y$, where $\mathrm{i}=\sqrt{-1}$, satisfies the condition $|z+1|=1$, then $z$ lies on
  1. X -axis.
  2. circle with centre $(1,0)$ and radius 1 unit.
  3. circle with centre $(-1,0)$ and radius 1 unit.
  4. Y-axis.

Solution

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

Asked in: MHT CET 2024 (15 May Shift 2)

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