When you are dividing, you can not have an imaginary number in the denominator (bottom of the fraction), just like you cannot have a radical in the denominator. To get rid of it, you multiply both the top and the bottom by 8i so you will get:
{(-1 - 2i)(8i)}/{(8i)(8i)}
On the top you must distribute the 8i so you get -8i -16i^{2}. Since i^{2 }is really -1, you get -8i - (-16) which is -8i +16, or in a + bi format, 16 -8i.
On the bottom you get 64i^{2 }and again, since i^{2 }is -1, you get -64.
This leaves you with (16 -8i)/-64.
Since all of these terms have a common factor, we can factor out a -8. When we do this we get:
(-2 + i)/8
in a + bi format this would be -2/8 + i/8 where the first fraction can again be reduced to -1/4.
This would mean a = -1/4 and b= 1/8