Hi all,

I edited the question and provide additional information .

Following is my complete code

> e0 := -21+.7*I;
                          
> e2 := e0;
                          
> e1 := 2.31;
                              
> e3 := 1;
                               
> t1 := 10*10^(-9);
                             
> t2 := 50*10^(-9);

> lambda:= 780*10^(-9);

> k0 := (2*3.14)/lambda;
                               
> g0 := sqrt(e0*k0^2-x^2);
                                     
> g1 := sqrt(e1*k0^2-x^2);
                         
> g2 := g0;
                                 
> g3 := sqrt(e3*k0^2-x^2);
                             
> theta1 := 0+I*g1*t1;
                                    
> theta2 := 0+I*g2*t2;
                                                    
> m := (e2*g3-e3*g2)*(e1*g2+e2*g1)*(e0*g1-e1*g0)*exp(theta1+theta2)+

(e2*g3-e3*g2)*(e1*g2-e2*g1)*(e0*g1+e1*g0)*exp(theta2-theta1)+

(e2*g3+e3*g2)*(e1*g2-e2*g1)*(e0*g1-e1*g0)*exp(theta1-theta2)+

(e2*g3+e3*g2)*(e1*g2+e2*g1)*(e0*g1+e1*g0)*exp(-theta1-theta2);

>fsolve(m = 0, x, x =1*10^5+1*10^4*I..1*10^7+1*10^7*I, complex);

The equation m=0 is obtained by analylical caculations and there will be infinite solutions.

I required only first 10 solutions and all are of complex roots.Since roots are complex,

the range must be complex.But i cannot specifically suggest the range of roots.

  The range format is like this 1*10^5+1*10^4*I..1*10^7+1*10^7*I.

  Complex root with lowest imaginary part will me my required first root and it's increasing

order determines the other roots that i required. Which means set that lie close to real 

axis are the most important ones.

Thanks