Addition is an arithmetic operation denoted by a plus sign + which represents the putting of objects into a collection.

$$OO\ + \ OOO\ = OOOOO$$

Commutativity and Associativity¶

Addition is an operation that is said to be both commutative and associative. These are two fundamental properties of addition that

For an operation to be commutative it must be true that $a + b = b + a$. This is simple enough for us to test:

$$1 + 2 \stackrel{?}{=} 2 + 1 \\ 3 = 3$$

For an operation to be associative, it must be true that $(a+b)+c=a+(b+c)$. Again, simple to show:

$$(1+2)+3\stackrel{?}{=}1+(2+3)\\(3)+3\stackrel{?}{=}1+(5)\\6=6$$

Addition of Complex Numbers¶

Addition of complex numbers is simple: you simply add the real and complex parts seperately.

$$(a+bi) + (c+di) = (a+c)+(b+d)i$$