Question

How do you simplify `(4+2i)(-5+2i)`?

Answer 1

`(4+2i)(-5+2i) = -24 -2i`

Explanation:

We simplify the multiplication of complex numbers by doing the multiplication like a binomial - i.e. we distribute the multiplication over the summed terms:

`(4+2i)(-5+2i) = 4(-5) + 4(2i)+2i(-5)+2i(2i)`
`(4+2i)(-5+2i) = -20 +8i -10i+4i^2`

now we collect like terms and use `i^2 =-1`

`(4+2i)(-5+2i) = -20 -2i+4(-1)`
`(4+2i)(-5+2i) = -20 -2i-4`

Finally,

`(4+2i)(-5+2i) = -24 -2i`