Alright so I posted a picture asking the exact question.(adsbygoogle = window.adsbygoogle || []).push({});

Here is my best attempt...

According to my professor's terrible notes, the numerator can magically turn into the form:

e^i(z+3)

when converted to complex. The denominator will be factored into

(z-2i)(z+2i)

but the function is only holomorphic at z=2i so only (z+2i) can be used.

From there the Res(f,2i)=g(2i) which is equal to what I believe is something like

e^(i(2i+3)/(4i)

It follows that

J=e^(-2+3i)*Pi

and sovling for the real part gives me an incorrect answer.

I might be missing some steps but I'm going off a theorem and it's really hard to relate to this problem. Help me PLEASE!

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

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!

# Cauchy Residual Theorem

Loading...

Similar Threads - Cauchy Residual Theorem | Date |
---|---|

A Residuals summing to zero? | May 15, 2017 |

A Cauchy convolution with other distribution | Jul 18, 2016 |

Variance and Cauchy Distribution | Apr 17, 2015 |

Pathological PDFs. eg: ratio of normals including Cauchy. | Jul 30, 2012 |

Statistics: Show that the sum of two independent Cauchy random variables is Cauchy. | Feb 15, 2012 |

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