[itex](1-z^3)^{1/2}[/itex] has three branch points at [itex]z=1, z=\omega[/itex]and [itex]z=\omega^2[/itex] where [itex]\omega = e^{2\pi i/3}[/itex](adsbygoogle = window.adsbygoogle || []).push({});

The branch points are the zeros of the function correct?

So why are not [itex]z=\omega^4[/itex], [itex]z=\omega^6[/itex], [itex]z=\omega^8[/itex] etc also branch points as they are zeros of the function?

as

[itex](e^{2\pi i/3^3})^6[/itex] =[itex]e^{2\pi i^6}[/itex] = [itex]e^{12\pi i}[/itex] = 1 so all even numbered powers of [itex]\omega[/itex] are zeros of the function

also why does the latex code move around vertically like this?

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# Help on Branch Points

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