Write ${2-i} \over {-1-5i}$ in factored form?

Question

Trying to help someone study for a final exam. My background: Calculus 1, Statistics.

I haven't done this kind of math in ages. Considering $i$ is $\sqrt{-1}$, I was thinking rationalize the denominator?

Answer 1

Yes: multiply the numerator and denominator by $-1+5i$.

$${{2-i} \over {-1-5i}} \cdot \frac{-1+5i}{-1+5i} = \frac{(2-i)(-1+5i)}{1+25}$$

Now expand the numerator and simplify.