The Fundamental Theorem of Algebra pp 5-20 | Cite as

# Complex Numbers

## Abstract

- (1)
Addition is commutative: a +b = b + a for each pair a, b in F.

- (2)
Addition is associative: a + (b + c) = (a + b) + c for a, b, c ∈ F.

- (3)
There exists an additive identity, denoted by 0, such that a + 0 = a for each a ∈ F.

- (4)
For each a E F there exists an additive inverse denoted —a, such that a + (-a) = 0.

- (5)
Multiplication is associative: a(bc) = (ab)c for a, b, c ∈ F.

- (6)
Multiplication is distributive over addition: a(b + c) = ab + ac for a, b, c ∈ F.

- (7)
Multiplication is commutative: ab = ba for each pair a, b in F.

- (8)
There exists an multiplicative identity denoted by 1 (not equal to 0) such that al = a for each a in F.

- (9)
For each a ∈ F, with a ≠ 0 there exists a multiplicative inverse denoted by a-1, such that aa

^{-1}= 1.

### Keywords

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