# Finding the zeros of a complex function in PyLab

1. Jun 22, 2014

### PeteyCoco

I have this characteristic equation for the wave number eigenvalues $k_n$ of a homogeneous infinte cylinder of radius R:

$D_{m} = (k_n R) = 0,$

where

$D_m (z) = n_r J'_m(n_r z)H_m(z) - J_m(n_r z)H'_m(z)$

and $n_r$ is the refractive index of the cylinder, the bessel and hankel functions are both of the first kind, and z is a complex argument. I'm not sure how I can solve for the zeros of this. I've been using PyLab, but haven't found any clues as to what I should do.

The article I'm working from is: http://arxiv.org/abs/1302.0245
These are equations (18) and (19) from the article

I'm new to this, so I may be trying something ridiculous.

2. Jun 23, 2014

### PeteyCoco

An even simpler statement of my problem: How can I find the zeros of a complex function in PyLab? Most sources I've found haven't helped.