\begin{definition}[Definition:Multiplication/Complex Numbers]
The '''multiplication operation''' in the domain of complex numbers $\C$ is written $\times$.
Let $z = a + i b, w = c + i d$ where $a, b, c, d \in \R$.
Then $z \times w$ is defined as:
:$\paren {a + i b} \times \paren {c + i d} = \paren {a c - b d} + i \paren {a d + b c}$
This follows by the facts that:
:Real Numbers form Field and thus real multiplication is distributive over real addition
:the entity $i$ is such that $i^2 = -1$.
\end{definition}