[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?

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Help on Branch Points

Loading...

Similar Threads for Help Branch Points | Date |
---|---|

B Need some help with understanding linear approximations | Feb 17, 2018 |

I Drawing the contour with a branch cut | Dec 6, 2017 |

I Help with simplifying series of hyperbolic integrals | Nov 19, 2017 |

I Help with understanding inexact differential | Nov 13, 2017 |

I Help please with biocalculus question involving differentiation | Nov 4, 2017 |

**Physics Forums - The Fusion of Science and Community**