# Moebius transformations mapping a doubly connected domain to an annulus

What are the Moebius transformations mapping the unbounded doubly connected domain in the extended complex plane, whose boundary consists of the circles $C_1:=\lbrace z\in\mathbb{C}:|z-5|=4\rbrace$ and $C_2:=\lbrace z\in\mathbb{C}:|z+5|=4\rbrace$, onto some annulus $\lbrace w\in\mathbb{C} : 1<|w|<R\rbrace$ ?

I also want to know whether any arbitrary multiply connected domains can be mapped to an annulus or not. If not what property should the domain satisfy in order to make this happen ?

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