Question

If the complex number $z=x+iy$ satisfies the condition $|z+1|=1$ , then $z$ lies on

• A. Circle with centre $(-1,0)$ and radius $1$
• B. $y-$axis
• C. none of these
• D. $x-$axis

Answer 1

The correct option is A Circle with centre $(-1,0)$ and radius $1$

$\because |z+1|=1$

$\Rightarrow |x+iy+1|=1$

$\Rightarrow |x+1+iy|=1$

$\Rightarrow \sqrt{(x+1{)}^2+y^2}=1$

$\Rightarrow (x+1{)}^2+y^2=1^2$

(squaring both sides)

Clearly, above equation represents the equation of a circle.

Centre $(-1,0)$ and radius $=1$

Hence, option (B) is correct.