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 $A\cup B$  is:

Correct Option - 4


Detailed Solution:

$\left|\frac{z+1}{z-1}\right|<1\Rightarrow \left|z+1\right|<\left|z-1\right|\Rightarrow Re\left(z\right)<0$

and $arg\left(\frac{z-1}{z+1}\right)=\frac{2\pi }{3}$  is a part of circle as shown.

 

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