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

a portion of a circle centred at $\left(0,-\frac{1}{\sqrt{3}}\right)$ that lies in the second quadrant only

a portion of a circle of radius $\frac{2}{\sqrt{3}}$ that lies in the third quadrant only

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

an empty set