Dividing complex numbers has a trick to it.
first thing to realize is that it's always easier to multiply than to divide. Doing so simplyfies your problem.
for example, if you have a simple division as such:
$ \frac{5}{\sqrt{2}} $
it would be easier to solve if you multiply by:
$ \frac{5}{\sqrt{2}} * \frac{\sqrt{2}}{\sqrt{2}} = \frac{5}{2} * \sqrt{2} $
With complex numbers, say you want to divide $ \frac{(2 + i)}{3 - i} $
it would be suitable to multiply top and bottom by the complex conjugate of the denominator.
$ \frac{(2 + i)}{3 - i} * \frac{(3 + i)}{3 + i} $
this would give a $ 10 $ in the denominator.
simplifying the expression into:
$ \frac{5 + 5i}{10} $ or $ \frac{1 + 1i}{2} $
which is the solution!
