Simplify $(2-2i)(5+5i)$, where $i^2 = -1.$
To simplify a product of complex numbers, I can use the distributive property and combine like terms. I get $(2-2i)(5+5i) = 2(5+5i) - 2i(5+5i) = 10 + 10i - 10i - 10i^2.$ Now I can simplify the terms involving $i^2$ by substituting $-1$ for $i^2.$ I get $10 + 10i - 10i - 10i^2 = 10 + 10i - 10i + 10 = 20.$ 