Prove the following facts about complex numbers:

(a) \(u+v=v+u\) for all \(u, v \in \mathbb{C}\).

(b) \(u v=v u\) for all \(u, v \in \mathbb{C}\).

(c) \((u+v)+w=(u+v)+w\) for all \(u, v, w \in \mathbb{C}\).

(d) \(u(v+w)=u v+u w\) for all \(u, v, w \in \mathbb{C}\).

(e) \(u(v w)=(u v) w\) for all \(u, v, w \in \mathbb{C}\).