Let $A = \left\{ z \in C : \left| \frac { z + 1 } { z - 1 } \right| < 1 \right\}$ and $B = \left\{ z \in C : \arg \left( \frac { z - 1 } { z + 1 } \right) = \frac { 2 \pi } { 3 } \right\}$. Then $A \cap B$ is (1) a portion of a circle centred at $\left( 0 , - \frac { 1 } { \sqrt { 3 } } \right)$ that lies in the second and third quadrants only (2) a portion of a circle centred at $\left( 0 , - \frac { 1 } { \sqrt { 3 } } \right)$ that lies in the second quadrant only (3) an empty set (4) a portion of a circle of radius $\frac { 2 } { \sqrt { 3 } }$ that lies in the third quadrant only
Let $A = \left\{ z \in C : \left| \frac { z + 1 } { z - 1 } \right| < 1 \right\}$ and $B = \left\{ z \in C : \arg \left( \frac { z - 1 } { z + 1 } \right) = \frac { 2 \pi } { 3 } \right\}$. Then $A \cap B$ is\\
(1) a portion of a circle centred at $\left( 0 , - \frac { 1 } { \sqrt { 3 } } \right)$ that lies in the second and third quadrants only\\
(2) a portion of a circle centred at $\left( 0 , - \frac { 1 } { \sqrt { 3 } } \right)$ that lies in the second quadrant only\\
(3) an empty set\\
(4) a portion of a circle of radius $\frac { 2 } { \sqrt { 3 } }$ that lies in the third quadrant only