Question

State True and False

$|z-i|<1$ represents all points z inside the circle with centre i.e.(0, 1) and radius 1.

Answer 1

$|z-i|=1$ represents a circle centered at i in Argand diagram that is, centered at $(0,1)$
Hence
$|z-i|<1$
Implies
$|x+i(y-1)|<1$
or
$x^2+(y-1{)}^2<1$ represents the points inside the circle described by
$|z-i|=1$
Or
$x^2+(y-1{)}^2=1$.