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) > 0or-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