" (iii) "arg(z-1)/(z+1)=(pi)/(2)

If arg((z-1)/(z+1))=(pi)/(2) then the locus of z is

Let z be a complex number and i=sqrt(-1) then the number of common points which satisfy arg(z-1-i)=(pi)/(6) and arg((z-1-i)/(z+1-i))=(pi)/(2) is

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.

If z = x + iy and arg ((z-1)/(z+1))=pi/2 , show that x^(2)+y^(2)-1=0 .