I am having a problem with a Complex Analysis question. It goes as follows:
Find a general Möbius Transformation $w=Tz$ that maps $\mathbb{A} = \{ z : |z-a|\leq R \}$ into $\mathbb{B} = \{ w : Re(w) \leq -3\}$.
So from my knowledge, I have to set up a generic Möbius Transformation function, say $w=\dfrac{az+b}{cz+d}$ and find the appropriate $a,b,c,d$. And to do that I have to specify three points of $z$.
How would I go about choosing the points and solve the question? Because the question says find general Möbius Transformation, I am having trouble starting the question.. Any hint would be appreciated.