Definition:Complex Number/Definition 2/Scalar Product

Definition

Let $\tuple {x, y}$ be a complex number.

Let $m \in \R$ be a real number.

Then $m \tuple {x, y}$ is defined as:

$m \tuple {x, y} := \tuple {m x, m y}$

Also see

• Definition:Complex Multiplication

• Results about complex multiplication can be found here.

Sources

• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Axiomatic Foundations of the Complex Number System: $\text {C}$. Product