How Do You Multiply Complex Numbers Using FOIL?

'i' is the imaginary unit and is equal to the square root of -1
We can treat complex numbers like binomials and multiply them using FOIL
Squaring 'i' is the same as squaring the square root of -1, which gives us just -1
We can replace i² with -1, so multiplying 10 by -1 gives us -10
Terms with 'i' in them are considered like terms, so we can combine them as if 'i' were a variable

1. Be careful -- 'i' is NOT a variable
2. 'i' is the imaginary unit and is equal to the square root of -1
3. But we can treat it like a variable when we're multiplying complex numbers
1. One way we can multiply binomials is using the FOIL method
2. We can do the same thing with complex numbers
1. FOIL stands for First, Outer, Inner, Last
2. This tells us which terms we need to multiply together
3. Remember, 'i' is the imaginary unit and is equal to the square root of -1
4. 'i' is NOT a variable - but when we multiply we can treat it like one
1. 'i' is NOT a variable!
2. It's just the letter we use to represent the square root of -1
3. But since it always has the same value, it is NOT a variable
4. Since 'i' just equals √(-1), when we square 'i' it's the same as squaring a square root
5. That means the square root will cancel out, and we're left with what was underneath: -1!
1. So instead of 10i², we could write 10•(-1)
2. 10•(-1) is just -10, so we can replace 10i² with -10
1. Even though 'i' is not a variable, again we can treat it like one when we combine like terms
2. Terms with an 'i' in them are considered like terms, so we can combine them like we would terms with variables
1. 'i' is equal to the square root of -1
2. Terms with 'i' in them are considered like terms, so we can combine them as if 'i' were a variable

Multiply 3 + 2i and 4 + 5i.