Mathematics - Complex Number Question with Solution | TestHub

$S_1:x^2+y^2\le \mathrm{25...}(1)$ $\begin{array}{rl}& S_2:\mathrm{lm}\text{ of }\frac{z+(1-\sqrt{3}i)}{(1-\sqrt{3}i)}\ge 0\\ & \mathrm{lm}\text{ of }\left(\frac{x+iy}{1-\sqrt{3}i}+1\right)\ge 0\\ & \mathrm{lm}\text{ of }\left(\frac{(x+iy)(1+\sqrt{3}i)}{4}\right)\ge 0\\ & \Rightarrow \sqrt{3}x+y\ge \mathrm{0...}(2)\\ & S_3:x\ge \mathrm{0...}(3)\\ & \text{ Area }=\frac{5}{12}\left(\pi (5{)}^2\right)\end{array}$