Complex addition


Definition

$$(a + ib) + (c + id) = (a + c) + i(b + d)$$
THEOREM   

Complex addition is commutative.

$$\forall x,y \in \mathbb{C} : x + y = y + x$$

Proof available

THEOREM   

Complex addition is associative.

$$\forall x,y,z \in \mathbb{C} : x + y + z = x + (y + z)$$

Proof available

LEMMA   

Zero is a left-identity element of complex addition.

$$\forall x \in \mathbb{C} : 0 + x = x$$

Proof available

LEMMA   

Zero is a right-identity element of complex addition.

$$\forall x \in \mathbb{C} : x + 0 = x$$

Proof available

THEOREM   

Zero is the identity element of complex addition.

Proof unavailable

Parent topics