# 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 $1 + 0 \, i$.

## Sources

- 1978: John S. Rose:
*A Course on Group Theory*... (previous) ... (next): $0$: Some Conventions and some Basic Facts