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Question

Let $A = \left\{ {z \in C:\left| {{{z + 1} \over {z - 1}}} \right| < 1} \right\}$ and $B = \left\{ {z \in C:\arg \left( {{{z - 1} \over {z + 1}}} \right) = {{2\pi } \over 3}} \right\}$. Then A $\cap$ B is :

a portion of a circle centred at $\left( {0, - {1 \over {\sqrt 3 }}} \right)$ that lies in the second and third quadrants only
a portion of a circle centred at $\left( {0, - {1 \over {\sqrt 3 }}} \right)$ that lies in the second quadrant only
an empty
a portion of a circle of radius ${2 \over {\sqrt 3 }}$ that lies in the third quadrant only

Solution

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