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Let $$f(z)=\frac{z-a}{z-b}$$ with $a,b\in D(0,r)$ and $r>0$. Let $$E=\{z\in\mathbb C: f(z)\notin N\}$$

$$N=\{Re(z)\leq 0;Im(z)=0\}$$

How can i find $E$ in terms of $r$?

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