Definition:Field of Complex Numbers
Jump to navigation
Jump to search
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
- 1964: Iain T. Adamson: Introduction to Field Theory ... (previous) ... (next): Chapter $\text {I}$: Elementary Definitions: $\S 1$. Rings and Fields: Example $2$
- 1974: Robert Gilmore: Lie Groups, Lie Algebras and Some of their Applications ... (previous) ... (next): Chapter $1$: Introductory Concepts: $1$. Basic Building Blocks: $3$. FIELD
- 1978: John S. Rose: A Course on Group Theory ... (previous) ... (next): $0$: Some Conventions and some Basic Facts
- 1998: Yoav Peleg, Reuven Pnini and Elyahu Zaarur: Quantum Mechanics ... (next): Chapter $2$: Mathematical Background: $2.1$ The Complex Field $C$