The locus of a point z in complex plane satisfying the condition `arg((z-2)/(z+2)) = pi/2` is

The locus of the points z satisfying the condition arg ((z-1)/(z+1))=pi/3 is, a

The locus of the points z satisfying the condition arg ((z-1)/(z+1))=pi/3 is, a

The complex number z satisfying the condition arg{(z-1)/(z+1)}=(pi)/(4) lies on

A(z_(1)) and B(z_(2)) are two given points in the complex plane. The locus of a point P(z) in the complex plane satisfying |z-z_(1)|-|z-z_(2)| ='|z1-z2 |, is

Show that the complex number z, satisfying the condition arg((z-1)/(z+1))=(pi)/(4) lie son a circle.