Argument of Negative Real Number is Pi

Theorem
Let $x \in \R_{>0}$ be a positive real number.

Then:
 * $\arg \paren {-x} = \pi$

where $\arg$ denotes the argument of a complex number.

Proof
We have that:
 * $-x = -x + 0 i$

and so:

Hence:

Hence:
 * $\arg \paren {-x} = \pi$