Thread: Complex Analysis - Value of Arg[(z-1)/(z+1)] between -pi and pi

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

Originally Posted by habsfan31

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[/FONT]

Know that

Originally Posted by Plato

Know that

I understand what you did, but not sure why you did it and what im supposed to do next.

Originally Posted by habsfan31

but not sure why you did it and what im supposed to do next.

I did it to answer the question:
Do you understand that is a real number?
Do you understand that
Do you understand that if then

Because and
then

Got it thanks!