Question

State True and False

$|z-3|=1$ represents all points z on the boundary of a circle with centre i.e .(3, 0) and radius 1.

Answer 1

$|z-3|=1$
put $z=x+iy$ in $|x+iy-3|=1$
$\Rightarrow {(x-3)}^2+{(y-0)}^2=1$
Therefore, locus of $z$ is circle with center $(3,0)$ with radius unity.