Definition:Complex Number/Definition 2/Multiplication

Definition

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:

$\tuple {x_1, y_1} \tuple {x_2, y_2} := \tuple {x_1 x_2 - y_1 y_2, x_1 y_2 + y_1 x_2}$

Also see

• Definition:Complex Addition

• Results about complex multiplication can be found here.

Sources

• 1957: E.G. Phillips: Functions of a Complex Variable (8th ed.) ... (previous) ... (next): Chapter $\text I$: Functions of a Complex Variable: $\S 1$. Complex Numbers: $\text {(iii)}$ The fundamental operations $(4)$
• 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 1.2$. The Algebraic Theory
• 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Chapter $\text{II}$: Groups: Subgroups
• 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