ThmDex – An index of mathematical definitions, results, and conjectures.
F127
Formulation 0
Let $\mathbb{C}$ be the D372: Set of complex numbers.
Let $+$ be the D606: Real addition operation.
Let $\cdot$ be the D610: Real multiplication operation.
The complex multiplication operation is the D554: Binary operation \begin{equation} \mathbb{C} \times \mathbb{C} \to \mathbb{C}, \quad ((a, b), (c, d)) \mapsto (a c - b d, a d + b c) \end{equation}