In a text I am reading occured the reflection in the line $\Bbb R^d z$:
For a fixed $z\in\Bbb R ^d $ we define $$T_z : \Bbb R^d \to \Bbb R ^d , T_z (x) := 2\langle x,z_0 \rangle z_0 - x$$ where $z_0 := \frac z {\Vert z \Vert}$. Now there was stated the following: Let $x\in\Bbb R^d$, then
$$\text{arg}(T_z (x)) = 2\text{arg}(z) - \text{arg}(x).$$ What is $x\mapsto \text{arg}(x)$?