Determine the transformations of $\frac{2-z}{iz-2}$.
I know there must be a way to get rid of one of the z's, but I do not know how. The closest bit of information is that we can express $\frac{2z+2}{iz+1}$ as $-2i+\frac{2+2i}{iz+1}$, but I do not know how my professor got to that. Once I get to one z, I know to convert to polar form and from there I can determine it. I just need to get rid of a z.
Can anyone help me, please?