Question

The complex number $z = x + iy$ which satisfies the equation $| z + 1 | = 1$ lies on

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

Answer 1

Answer: (B)

a circle with $(-1, 0)$ as the centre and radius $1$

Answer 2

$\left|z+1\right|\left|x+iy+1\right|=1$ $\Rightarrow \left(x+1\right)^{2}+y^{2}=1$ which is a circle with centre $(-1, 0)$ and radius $1$.