Definition:Field of Complex Numbers

Definition
The field of complex numbers $\left({\C, + \times}\right)$ is the set of complex numbers under the two operations of addition and multiplication.

Also see

 * Complex Numbers form Field

Thus:
 * $\left({\C, +}\right)$ is the additive group of complex numbers
 * $\left({\C_{\ne 0}, \times}\right)$ is the multiplicative group of complex numbers
 * The zero of $\left({\C, + \times}\right)$ is $0 + 0 \, i$
 * The unity of $\left({\C, + \times}\right)$ is $1 + 0 \, i$.