Find the locus of z if arg `((z-1)/(z+1))= pi/4`

Represents the variable complex number z . Find the locus of P if arg((z-1)/(z+3))=(pi)/(2) .

Statement-1 : The locus of z , if arg((z-1)/(z+1)) = pi/2 is a circle. and Statement -2 : |(z-2)/(z+2)| = pi/2 , then the locus of z is a circle.

Statement-1 : The locus of z , if arg((z-1)/(z+1)) = pi/2 is a circle. and Statement -2 : |(z-2)/(z+2)| = pi/2 , then the locus of z is a circle.

Trace the locus of z if arg(z+i)=(-pi)/(4)

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