Question

Find the points of the plane which satisfy the following inequalities.
$1<|2z-6|<2.$

Answer 1

$1<2z-6<2$

$\Rightarrow \frac{1}{2}<|z-3|<1$ [Dividing by $2$]

$\Rightarrow \frac{1}{4}<{|z-3|}^2<1$

$\frac{1}{4}<{(a-3)}^2+b^2<1$

${(a-3)}^2+b^2<1$

${(a-3)}^2+b^2>\frac{1}{4}$