Definition:Multiplication/Complex Numbers

Definition
The multiplication operation in the domain of complex numbers $\C$ is written $\times$.

Let $z = a + i b, w = c + i d$ where $a, b, c, d \in \R$.

Then $z \times w$ is defined as:
 * $\paren {a + i b} \times \paren {c + i d} = \paren {a c - b d} + i \paren {a d + b c}$

This follows by the facts that:
 * Real Numbers form Field and thus real multiplication is distributive over real addition
 * the entity $i$ is such that $i^2 = -1$.

Complex Multiplication
When the formal definition of complex numbers is used, complex multiplication is defined thus:

Also see

 * Complex Multiplication is Commutative
 * Complex Multiplication is Associative


 * Definition:Complex Addition