Question

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

Answer 1

`12-8i`

Explanation:

Like we would do with real numbers, we can multiply this out with FOIL (Firsts, Outsides, Insides, Lasts). This is the order we multiply in. We get

• First terms: `-5*-2=10`
• Outside terms: `-5*2i=-10i`
• Inside terms: `-i*-2=2i`
• Last terms: `-i*2i=-2i^2`

This leaves us with

`-2i^2-10i+2i+10`

Which can be simplified further as

`-2i^2-8i+10`

Note that `i^2=-1`, so we can plug in this value. We now have

`-2(-1)-8i+10`

Which finally simplifies to

`12-8i`

Hope this helps!