You can still use synthetic division to divide $\displaystyle (x^2 + 4) \div (x-2i)$:

Code:

2i| 1 0 4
-- 2i -4
------------
1 2i 0

So the quotient, as Prove It has shown, is $\displaystyle x + 2i$.

For the second problem, I'm guessing that you're being asked to show that

$\displaystyle (x^3 -3x^2 +x -3) \div (x - 3)$ has no remainder. The setup would be like this:

Code:

3| 1 -3 1 -3
--
--------------
1

I'll let you do the rest. If you're stuck, look at this tutorial on synthetic division here: Synthetic Division .

01