I have this question I am suppose to solve and I think i misunderstood something. It is in a University algebra book and the questions is:

Show that if abs:z =1 then, abs:$\displaystyle \left[\frac{2z-1}{z-2}\right]=1$

I dont see what is so difficult here?? why, why put this into a University book??

If abs:z=1 then, abs:2z-1=1 and in the nominator abs:z-2 = -1 and absolute value of that is 1. So it is $\displaystyle \frac{1}{1}$?

Have I missunderstood something?