Question

State True and False

$|i-1-2z|>9$ represents all points $z$ which lies outside the circle with center $(-\frac{1}{2},\frac{1}{2})$ and radius $\frac{9}{2}$.

Answer 1

The inequality can be written as $|-2||z-\frac{i-1}{2}|>9$
$|z-\frac{i-1}{2}|>\frac{9}{2}$ which represents all points z outside the circle with centre $\frac{(i-1)}{2}$ or $(-\frac{1}{2},\frac{1}{2})$ and radius $\frac{9}{2}.$