Question

How do you Multiply Complex Numbers? I used a calculator that shows work and it mentioned something called the foil method which gave -20+16i+15i+12 when I put (4-3i)(-5+4i). What is the foil method

Answer 1

The FOIL method is the formula that is used when multiplying 2 binomials, where

(a+b)(c+d) = a(c+d) + b(c+d) =  ac + ad + bc + bd

Using the formula above, apply the foil method.

4(-5+4i) - 3i(-5+4i)

4(-5) + 4(4i) + (-3i(-5)) + (-3i(4i))

-20 + 16i + (15i) + (-12i^2)

-20 + 16i + 15i - 12i^2

Since i^2 = -1, then

-20 + 16i + 15i - 12(-1)

-20 + 16i + 15i + 12

Hope this helps.