Definition:Field of Complex Numbers

Definition

The field of complex numbers $\struct {\C, + \times}$ is the set of complex numbers under the two operations of addition and multiplication.

Also see

Thus:

$\struct {\C, +}$ is the additive group of complex numbers
$\struct {\C_{\ne 0}, \times}$ is the multiplicative group of complex numbers
The zero of $\struct {\C, + \times}$ is $0 + 0 \, i$
The unity of $\struct {\C, + \times}$ is $1 + 0 \, i$.