# 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 38 subcategories, out of 38 total.

### A

### C

### E

### F

### G

### H

### P

### S

### T

## Pages in category "Complex Numbers"

The following 75 pages are in this category, out of 75 total.

### A

### C

- Characteristic of Subfield of Complex Numbers is Zero
- 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 Totally Ordered
- 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 under Addition form Abelian Group
- Complex Numbers under Addition form Group
- Complex Numbers under Addition form Monoid
- Complex Numbers under Multiplication do not form Group
- Complex Numbers under Multiplication form Monoid
- 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

### E

### G

### H

### I

### M

### N

### P

- Pointwise Addition on Complex-Valued Functions is Associative
- Pointwise Addition on Complex-Valued Functions is Commutative
- Pointwise Multiplication on Complex-Valued Functions is Associative
- Pointwise Multiplication on Complex-Valued Functions is Commutative
- Power Function on Complex Numbers is Epimorphism
- Powers of Imaginary Unit
- Properties of Complex Numbers