Method for solving complex equations f(z)=0

[liviuct]

Hey! Does anyone know any good method for solving complex equations of one complex variable? I found over the internet that I could use Newton's method, and I tried it for a common function, and it worked. Anyway, I'm not very pleased of Newton's method because of the use of the first aproximation value. Also it does not return all the solutions. I need it for calculating some resonances energies for my Bachelor Thesis in Quantum Mechanics.
I also tried methods for real functions (in order to integrate the Schrödinger Equations and obtaining the eigenvalues), like bisection method or Ridder's Method. They worked just fine.

Thank you.

 

[mathman]

For most equations you need a guess as an approximate solution or a bracket. Which method works best tends to be problem specific.