I am trying to understand how things work visually in the complex plane.

For example, I already got that the z -> 1/z transformation will turn |z|< 1 into |z|>1.

Now, it seems the z -> 1/(z-1) transformation will turn |z|<1 into |z-1|>1. But how can I picture z -> 1/(z-1) in |z-(1+2i)|=1? Is there any resource only that will help understanding this concepts? I'm having a hard time finding anything about it on google.