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I'm having trouble understanding the following:

Given a region of a circular wedge with endpoints [tex]a[/tex] and [tex]b[/tex], the mapping [tex]z_{1}=\frac{z-a}{z-b}[/tex] transforms this wedge into an angular sector. Then, by an appropriate power [tex]\alpha[/tex], the map [tex]w = z_{1}^\alpha[/tex] maps the angular sector onto a half plane. How exactly does this wedge turn into a nice angular sector just by [tex]z_1[/tex]?

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# Conformal map

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