Mathematics - Complex Number Question with Solution | TestHub

Put $z=x+iy$ $|z-1|\le 2\Rightarrow (x-1{)}^2+y^2\le 4$ ...(i) $\Rightarrow x-y\le 1$ ...(ii) $\mathrm{Im}(\mathrm{z})\ge 0\Rightarrow \mathrm{y}\ge 0$ ...(iii)
$\begin{array}{rl}& \text{ Required area }\\ & =\text{ Area of semi-circle }-\text{ area of sector A }\\ & \frac{1}{2}\pi (2{)}^2-\frac{\pi }{2}\\ & =\frac{3\pi }{2}\end{array}$