How Do You Add Complex Numbers?

'i' is the imaginary unit and represents the square root of -1, so it's NOT a variable
But even though 'i' is not a variable, we can treat it like one when we add
8 and 4 are like terms since they're both just constants
7i and 3i are also like terms since they both have a number times 'i'
Group the like terms together to make addition simpler
The Associative Property allows us to regroup our terms
The symbol over -1 is the square root symbol
7i+3i = 10i, just like 7x+3x = 10x

1. Our complex numbers are (8+7i) and (4+3i)
2. 'i' is the imaginary unit and represents the square root of -1, so it's NOT a variable
3. But even though 'i' is not a variable, we can treat it like one when we add
4. 8 and 4 are like terms since they both consist of one number
5. 7i and 3i are also like terms since they both have a number times 'i'
1. We just determined that 8 and 4 are like terms, and so are 7i and 3i
2. 'i' is the imaginary unit and represents the square root of -1, so it's NOT a variable
3. But even though 'i' is not a variable, we can treat it like one when we add
4. The Associative Property allows us to regroup terms, so we can put like terms together
1. Like terms can be combined, leaving you with fewer terms to work with!
2. 8+4 = 12
3. Although 'i' is not a variable, addition works just like it does with variables
4. So 7i+3i = 10i, just like 7x+3x = 10x

Add (8 + 7i) and (4 + 3i).