MHT CET · Maths · Complex Number
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.
- C circle with centre \((-1,0)\) and radius 1 unit.
- D Y-axis.
Answer & Solution
Correct Answer
(C) circle with centre \((-1,0)\) and radius 1 unit.
Step-by-step Solution
Detailed explanation
\(\begin{aligned}
& |\mathrm{z}+1|=1 \\
& \Rightarrow|x+\mathrm{i} y+1|=1 \\
& \Rightarrow(x+1)^2+y^2=(1)^2 \\
& \Rightarrow(x+1)^2+y^2=1
\end{aligned}\)
This is an equation of circle with centre \((-1,0)\) and radius 1 .
& |\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 .
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