If a Möbius transform is a map that goes from the extended complex plane to the extended complex plane, given by some $\omega = \frac{az + b}{cz + d}$, where $ad - bc \neq 0$. In my notes, underneath the definition, I have:
Ex: $ \frac{1z + 2}{2z + 4} = \frac{1}{2}$.
How does this work? Isn't ad - bc = 0? Or have I made some kind of mistake in writing down the notes properly? Where does the fraction come from?