-10-6i / -9+9i

If you mean (-10-6i) /( -9+9i) , then the brackets are essential

(-10-6i) /( -9+9i)
= (-10-6i) /( -9+9i) * (-9-9i)/(-9-9i)
= (90 + 90i + 54i + 36i^2)/(81 -81i^2)
= (54 + 144i)/162
= 1/3 + (8/9)i