Let $A, B, C$ be three sets of complex numbers as defined below $A=\{z: \operatorname{Im} z \geq 1\}

Question

Let $A, B, C$ be three sets of complex numbers as defined below $A=\{z: \operatorname{Im} z \geq 1\}$ $B=\{z:|z-2-i|=3\}$ $C=\{z: \operatorname{Re}((1-i) z)=\sqrt{2}\}$. The number of elements in the set $A \cap B \cap C$ is\

Professor PC Thomas Classes · Answer

(b) : In the cartesian co-ordinates sets $A, B$ and $C$ define the regions given by $A: y$ $\geq 1, B:(x-2)^{2}+(y-1)^{2}=9, C: x+y$\ $=\sqrt{2} B$ and $C$, being a circle and a straight line intersect in two points, out of which only one satisfies\ $y \geq 1$.\ Thus the number of elements in the set $A \cap$ $B \cap C$ is 1 .\