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
X -axis.
circle with centre $(1,0)$ and radius 1 unit.
circle with centre $(-1,0)$ and radius 1 unit.
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 .