# Category:Complex Numbers

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This category contains results about **Complex Numbers**.

Definitions specific to this category can be found in Definitions/Complex Numbers.

A **complex number** is a number in the form $a + b i$ or $a + i b$ where:

- $a$ and $b$ are real numbers
- $i$ is a square root of $-1$, that is, $i = \sqrt {-1}$.

## Subcategories

This category has the following 44 subcategories, out of 44 total.

### A

### C

- Circle Group is Group (5 P)
- Cosecant of i (3 P)
- Cosine of Complex Number (3 P)
- Cosine of i (3 P)
- Cotangent of Complex Number (4 P)
- Cotangent of i (3 P)
- Cross-Ratios (empty)
- Cyclotomic Rings (9 P)

### E

- Eisenstein Integers (2 P)

### F

- Field Norm of Complex Number (4 P)

### G

- Gaussian Rationals (2 P)

### H

### I

- Imaginary Parts (3 P)

### P

### R

- Real Parts (3 P)

### S

- Secant of i (3 P)
- Sine of Complex Number (3 P)
- Sine of i (3 P)

### T

- Tangent of Complex Number (5 P)
- Tangent of i (3 P)

## Pages in category "Complex Numbers"

The following 58 pages are in this category, out of 58 total.

### C

- Canonical Injection of Real Number Line into Complex Plane
- Characteristic of Subfield of Complex Numbers is Zero
- Circle Group is Group
- Circle Group is Infinite Abelian Group
- Complex Numbers are Uncountable
- Complex Numbers as External Direct Product
- Complex Numbers as Quotient Ring of Real Polynomial
- Complex Numbers cannot be Ordered Compatibly with Ring Structure
- Complex Numbers form Algebra
- Complex Numbers form Field
- Complex Numbers form Integral Domain
- Complex Numbers form Ring
- Complex Numbers form Subfield of Quaternions
- Complex Numbers form Vector Space over Themselves
- Complex Numbers with Complex Modulus form Normed Vector Space
- Complex Vector Space is Vector Space
- Convergence of Generalized Sum of Complex Numbers
- Convergence of Generalized Sum of Complex Numbers/Corollary
- Cosecant of Complex Number
- Cosecant of i
- Cosine of Complex Number
- Cosine of i
- Cotangent of Complex Number
- Cotangent of i