\begin{definition}[Definition:Addition/Complex Numbers]
The '''addition operation''' in the domain of complex numbers $\C$ is written $+$.
Let $z = a + i b, w = c + i d$ where $a, b, c, d \in \R, i^2 = -1$.
Then $z + w$ is defined as:
:$\paren {a + i b} + \paren {c + i d} = \paren {a + c} + i \paren {b + d}$
\end{definition}