(-5-i)(-2+2i)

Use the Foil method: first, outside, inside, and last

(-5 - i )(-2 + 2i)

-5*-2 = 10

-5(2i) = -10i

-i*-2 = 2i

-i(2i) = -2i^2 [i^2 = -1] --> -2(-1) = 2

Add all the terms together: 10 - 10i + 2i + 2 = 12 - 8i.