Question

Simplify the following quotient of complex numbers into the form a + bi.
-4-3i/2-i

Answer 1

Let's multiply by 1 in the form of 2+i/2+i.
That gives -4-3i/2-i x 2+i/2+i
Using foil, on top we get:
(-4-3i)x(2+i)
= -8 - 6i -4i - 3isquared
isquared = -1, so we get -8 - 10i +3
= -5 - 10i

Now on the bottom, we foil to get:
(2-i)(2+i)
= 4 -2i + 2i -isquared
= 4 + 1
= 5

So we have -5 - 10i/5
= -5/5 - 10i/5
= -1 - 2i