Let $S=S_{1} \cap S_{2} \cap S_{3}$, where $S_{1}=\{z \in C:|z|

Question

Let $S=S_{1} \cap S_{2} \cap S_{3}$, where $S_{1}=\{z \in C:|z|<4\}, S_{2}=\left\{z \in C: \operatorname{Im}\left[\frac{z-1+\sqrt{3} i}{1-\sqrt{3} i}ight]>0ight\}$ and $S_{3}=\{z \in C: \operatorname{Re} z>0\}$ Area of $S=$\

Professor PC Thomas Classes · Answer

(b): The curve $S_{1}$ is $x^{2}+y^{2}<16$\ $S_{2}$ turns out to be $\sqrt{3} x+y>0$\ And $S_{3}$ is $x>0$\  Area $=\frac{1}{2} r^{2} 	heta=\frac{1}{2} 	imes 16 	imes \frac{5 \pi}{6}=\frac{20 \pi}{3}$\