Solve complex roots for a dispersion equation with complex coefficients

Hello,

I am solving a equation as follows,

1=((n+N)/n) * k * tanh(k*h)

where N is a known complex number (e.g. 2+3i), h and n is two known real constants.

I am trying to solve the k, which are infinite complex roots (e.g. a+bi).

I was trying to use Newton-Raphson method to solve it. However, without a good guess, I couldn't get the solutions. Also, since there are infinite k, I have no idea how to give infinite initial guess.

I would appreciate any ideas. Thanks a lot.

[Matt Fig]

Show the values for N,n and h that you are using...