Mathematics - Complex Number Question with Solution | TestHub

Let $z=x+iy$
$\begin{array}{rl}& A:|z-2-i|=3\\ & |(x-2)+(y-1)i|=3\\ & (x-2{)}^2+(y-1{)}^2=\mathrm{9....}(1)\\ & B=\mathrm{Re}(z-iz)=2\\ & \mathrm{Re}((x+y)+i(y-x))=2\\ & x+y=\mathrm{2....}(2)\end{array}.$
On solving (1) and (2) we get
$\begin{array}{rl}& x=\frac{3\pm \sqrt{17}}{2},y=\frac{1\mp \sqrt{17}}{2}\\ & \sum _{z\in \mathrm{s}}|z{|}^2=\frac{1}{4}[2\times 26+2\times 18]\\ & \Rightarrow \frac{88}{4}=22\end{array}$