Q72 / 150 · MHT CET 2024 (15 May Shift 2) · Mathematics

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

  • A
    X -axis.
  • B
    circle with centre $(1,0)$ and radius 1 unit.
  • Correct answer
    C
    circle with centre $(-1,0)$ and radius 1 unit.
  • D
    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 .

Hence, the correct answer is option: 'C'.

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