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`

Show that the locus of z = x + iy such that the amplitude of (z -1)/(z+1) is equal to pi/4 . prove that x^2 + y^2 - 2y -1 =0

if argument of (z-1)/(z+1)=(pi)/(4) then prove that x^(2)+y^(2)-2y=1

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 .

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 .

if cos^(-1)x+cos ^(-1)y+cos^(-1) z=pi prove that x^(2) +y^(2)+z^(2) +2xyz=1

If cos^(-1)x+cos^(-1)y+cos^(-1)z=pi , prove that x^2+y^2+z^2+2x y z=1.

If cos^(-1)x+cos^(-1)y+cos^(-1)z=pi , prove that x^2+y^2+z^2+2x y z=1.

If complex number z=x +iy satisfies the equation Re (z+1) = |z-1| , then prove that z lies on y^(2) = 4x .

If complex number z=x +iy satisfies the equation Re (z+1) = |z-1| , then prove that z lies on y^(2) = 4x .