Mapping Real Axis and Im(z)=1 to Tangent Circles?

[Office_Shredder]

Homework Statement

Find a Mobius transformation that maps the real axis to the circle |z-1|=1, and the line Im(z)=1 to the circle |z-2|=1

Homework Equations

A mobius transformation is one of the form z\rightarrow\frac{az+b}{cz+d} on the extended complex plane

The Attempt at a Solution

My attempt pretty much comes out to... well, mobius transformations are bijections, but the two lines I'm given in the pre-image only intersect at infinity. So how do I get the two intersection for the circles? I'm thinking maybe I'm really dumb, and they're just tangent, but it looks to me as if they meet at \frac{3}{2}\pm\frac{\sqrt{3}}{2}i

 

[AKG]

You're right, there does seem to be a problem with the question.

 

[Office_Shredder]

I asked someone about it, and it's actually |z|=1 and |z-2|=1, so they're tangent at a point (I was reading off the circle descriptions from the question above previously... whoops).

I was having enough trouble with these stupid things without making them even more difficult for myself.