ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
▼ Alphabet
▼ Deduction system
▼ Theory
▼ Zermelo-Fraenkel set theory
▼ Set
▼ Binary cartesian set product
▼ Binary relation
▼ Map
▼ Operation
▼ N-operation
▼ Binary operation
▼ Enclosed binary operation
▼ Groupoid
▼ Ringoid
▼ Semiring
▼ Ring
▼ Additive group
▼ Additive monoid
▼ Additive semigroup
▼ Additive groupoid
▼ Additive binary operation
▼ Natural number addition operation
▼ Integer addition operation
▼ Rational addition operation
▼ Real addition operation
Definition D607
Complex addition operation
Formulation 0
Let $\mathbb{C}$ be the D372: Set of complex numbers.
Let $\pm$ be the D606: Real addition operation.
The complex addition operation is the D554: Binary operation \begin{equation} + : \mathbb{C} \times \mathbb{C} \to \mathbb{C}, \quad (a, b) + (c, d) = (a \pm c, b \pm d) \end{equation}