I'm looking at an integral which in part involves finding the residue of [tex]\frac{1}{1+z^{n}}[/tex] at [tex]z=e^{\frac{i\pi}{n}}[/tex](adsbygoogle = window.adsbygoogle || []).push({});

I thought the general method for residues was to find the 1/z term in the Laurent series, (which i'm not particularly sure how to do in this case), however, the answer provided does:

[tex]\frac{1}{\frac{d}{dz}(1+z^n)} = -\frac{1}{nz^{n-1}}[/tex]

evaluating this at [tex]z=e^{\frac{i\pi}{n}} [/tex], they obtain:

[tex]Res=-\frac{e^{\frac{i\pi}{n}}}{n}[/tex]

Why is this a legitimate method, for solving residues, can you always employ this method (it seems much easier), are there any other important methods for determining the residues of various things?

Thanks,

~Lyuokdea

**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!

# Evaluating Residues

Loading...

Similar Threads - Evaluating Residues | Date |
---|---|

I Evaluation of a line integral | Sep 14, 2017 |

I Evaluating improper integrals with singularities | Mar 15, 2017 |

I Can indeterminate limits always be evaluated? | Jan 23, 2017 |

I Evaluate using Leibniz rule and/or chain rule | Dec 6, 2016 |

Evaluating integrals using the residue theorem | Nov 13, 2007 |

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