Understanding $\text{Arg}(1+z) - \text{Arg}(1 - z)$

Question

I am wondering why $\frac{2}{\pi}[\text{Arg}(1+z) - \text{Arg}(1-z)]$ is equal to $u(z) = (2 \pi)(\varphi + \psi)$ where $\varphi$, $\psi$ are the angles represented in the figure. I normally think of adding complex numbers as vectors, and the picture doesn't make sense to me.

Answer 1

$1-z$ is the vector with tail at $z$ and head at $1.$

The argument is the angle that this vector forms with the x axis.

$Arg (1-z) = -\psi$

$1+z = z-(-1)$ is the vector with head at z and tail at $-1.$

$Arg (1+z) = \phi$