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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 [tex]z\rightarrow\frac{az+b}{cz+d}[/tex] 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 [tex]\frac{3}{2}\pm\frac{\sqrt{3}}{2}i[/tex]