Let $\mathbb{Z}$ be the D367: Set of integers.
Let $+$ be the D637: Natural number addition operation.
Let $\cdot$ be the D638: Natural number multiplication operation.
The integer multiplication operation is the D554: Binary operation \begin{equation} \mathbb{Z} \times \mathbb{Z} \to \mathbb{Z}, \quad [(a, b)] [(c, d)] = [(a c + b d, a d + b c)] \end{equation}

Let $\mathbb{Z}$ be the D367: Set of integers.
Let $+$ be the D637: Natural number addition operation.
Let $\cdot$ be the D638: Natural number multiplication operation.
The integer multiplication operation is the D554: Binary operation \begin{equation} \mathbb{Z} \times \mathbb{Z} \to \mathbb{Z}, \quad [(a, b)] [(c, d)] = [(a \cdot c + b \cdot d, a \cdot d + b \cdot c)] \end{equation}