Formalized electric field

[Draeden]

We have a complex function:

[tex]f:C\to C \\ f(z) = \sum_{n=1}^{m}\frac 1{z-a_n}[/tex]

Is there an easy way to determine all zeros, i.e. such [tex]z[/tex] where [tex]f(z)=0[/tex] ?
Would the problem appear easier if we assume that all [tex]a_n[/tex] are real ?