A variable complex number `z=x+iy` is such that arg `(z-1)/(z+1)= pi/2`. Show that `x^2+y^2-1=0`.

The complex number z satisfying |z+1|=|z-1| and arg (z-1)/(z+1)=pi/4 , is

If z=x+iy such that the argument of (z-1)/(z+1) is always (pi)/(4). Prove that x^(2)+y^(2)-2y=1

Let Z and w be two complex number such that |zw|=1 and arg(z)-arg(w)=pi/2 then

Statement-1 : let z_(1) and z_(2) be two complex numbers such that arg (z_(1)) = pi/3 and arg(z_(2)) = pi/6 " then arg " (z_(1) z_(2)) = pi/2 and Statement -2 : arg(z_(1)z_(2)) = arg(z_(1)) + arg(z_(2)) + 2kpi, k in { 0,1,-1}

If z and w are two complex number such that |zw|=1 and arg(z)arg(w)=(pi)/(2), then show that bar(z)w=-i

If z_(1)andz_(2) are two complex numbers such that |z_(1)|=|z_(2)| and arg(z_(1))+arg(z_(2))=pi, then show that z_(1),=-(z)_(2)

Find the complex number z if arg (z+1)=(pi)/(6) and arg(z-1)=(2 pi)/(3)

If z=x+iy such that |z+1|=|z-1| and arg((z-1)/(z+1))=(pi)/(4) then