\begin{definition}[Definition:Complex Number/Definition 2/Multiplication]
Let $\tuple {x_1, y_1}$ and $\tuple {x_2, y_2}$ be complex numbers.
Then $\tuple {x_1, y_1} \tuple {x_2, y_2}$ is defined as:
:$\tuple {x_1, y_1} \tuple {x_2, y_2} := \tuple {x_1 x_2 - y_1 y_2, x_1 y_2 + y_1 x_2}$
\end{definition}