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

The locus of the point satisfying the condition amp. ((z-1)/(z+1))=(pi)/(3) is

For a non-zero complex number z , let arg(z) denote the principal argument with -pi lt arg(z)leq pi Then, which of the following statement(s) is (are) FALSE? arg(-1,-i)=pi/4, where i=sqrt(-1) (b) The function f: R->(-pi, pi], defined by f(t)=arg(-1+it) for all t in R , is continuous at all points of RR , where i=sqrt(-1) (c) For any two non-zero complex numbers z_1 and z_2 , arg((z_1)/(z_2))-arg(z_1)+arg(z_2) is an integer multiple of 2pi (d) For any three given distinct complex numbers z_1 , z_2 and z_3 , the locus of the point z satisfying the condition arg(((z-z_1)(z_2-z_3))/((z-z_3)(z_2-z_1)))=pi , lies on a straight line

For a non-zero complex number z , let arg(z) denote the principal argument with pi lt arg(z)leq pi Then, which of the following statement(s) is (are) FALSE? arg(-1,-i)=pi/4, where i=sqrt(-1) (b) The function f: R->(-pi, pi], defined by f(t)=arg(-1+it) for all t in R , is continuous at all points of RR , where i=sqrt(-1) (c) For any two non-zero complex numbers z_1 and z_2 , arg((z_1)/(z_2))-arg(z_1)+arg(z_2) is an integer multiple of 2pi (d) For any three given distinct complex numbers z_1 , z_2 and z_3 , the locus of the point z satisfying the condition arg(((z-z_1)(z_2-z_3))/((z-z_3)(z_2-z_1)))=pi , lies on a straight line

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

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