Let Arg(w) denote that value of the argument between -π and π (inclusive). Show
that:
Arg[(z-1)/(z+1)] = { π/2, if Im(z) > 0 or -π/2 ,if Im(z) < 0.
where z is a point on the unit circle ∣z∣= 1.
My attempt: I know Arg[(z-1)/(z+1)] = Arg(z-1) - Arg(z+1) and the arg(w) = arctan(b/a), but im stuck.
Please help