how can i find complex roots of nonlinear equation?

[ehsan_faal]

hi there,
i have 2 equation that i must to find the complex roots of them,this is my code in matlab,i hope some one could help me.

Eq1=@(x) 1+1j.*epsilon.*cosh((N-3).*acosh((x./1j).*sqrt((Omega0^2 -1)./(Omega0^2 -(x./1j).^2)))+3.*acosh(x./1j));
Eq2=@(x) 1-1j.*epsilon.*cosh((N-3).*acosh((x./1j).*sqrt((Omega0^2 -1)./(Omega0^2 -(x./1j).^2)))+3.*acosh(x./1j));

A=linspace(-0.6,0.6,5e3);
B=linspace(-1.5,1.5,5e3);
[NA,NB]=meshgrid(A,B);
Count=1:numel(NA);
xData=complex(NA(Count),NB(Count));
EvalEquation1=Eq1(xData);
EvalEquation2=Eq2(xData);
Telorance=0.001;

SelectionO=find(real(EvalEquation1)<Telorance & imag(EvalEquation1)<Telorance & real(EvalEquation1)>-Telorance & imag(EvalEquation1)>-Telorance);
EvalEquation1N=Eq1(xData(SelectionO));
xDataNO=xData(SelectionO);
InputDataO=xDataNO(real(xDataNO)<0);
InputDataO=unique(InputDataO);
YO=poly(InputDataO);

SelectionE=find(real(EvalEquation2)<Telorance & imag(EvalEquation2)<Telorance & real(EvalEquation2)>-Telorance & imag(EvalEquation2)>-Telorance);
EvalEquation2N=Eq2(xData(SelectionE));
xDataNE=xData(SelectionE);
InputDataE=xDataNE(real(xDataNE)<0);
InputDataE=unique(InputDataE);
YE=poly(InputDataE);

but it seems not exactly the solution that used in this article,i want to achieve the answer that compute in this paper (page2):

https://s5.picofile.com/file/8144646942/A_Novel_Class_of_Generalized_Chebyshev.pdf.html

it is urgent ,please help