Question: How can I solve a set of equations that one of them has real and imaginary part ?

I solve a set of equations in this way and I have three set of answers ,but I don`t know wich one is true.

and I have another question ,how can I assume v[0] like a constant?

 

alpha[2]:= 2.727272728*10^5: alpha[4]:= 3738.685337: alpha[6]:= -30.18675539: alpha[7] := -4.116375735*10^6: alpha[8] := 1.859504132*10^10: alpha[9]:= 2.489142857*10^(-12):

l10:=(alpha[7]*v[0]^2+1)*gamma[i*n]^4+(-alpha[4]*beta[n]^2+alpha[8]*v[0]^2-alpha[9])*gamma[i*n]^2+(2*I)*gamma[i*n]*alpha[2]*beta[n]*v[0]+(2*I)*gamma[i*n]^3*alpha[6]*beta[n]*v[0]-beta[n]^2 = 0:

l11 := subs(i = 1, l10);

l12 := subs(i = 2, l10);

l13 := subs(i = 3, l10);

l14 := subs(i = 4, l10);

l15 := (exp(I*(gamma[n]+gamma[2*n]))+exp(I*(gamma[3*n]+gamma[4*n])))*(gamma[3*n]^2-gamma[4*n]^2)*(gamma[n]^2-gamma[2*n]^2)+(exp(I*(gamma[n]+gamma[4*n]))+exp(I*(gamma[2*n]+gamma[3*n])))*(gamma[2*n]^2-gamma[3*n]^2)*(gamma[n]^2-gamma[4*n]^2)+(exp(I*(gamma[2*n]+gamma[4*n]))+exp(I*(gamma[n]+gamma[3*n])))*(gamma[2*n]^2-gamma[4*n]^2)*(-gamma[n]^2+gamma[3*n]^2) = 0;

l1 := combine(expand(evalc(l15)), trig):

l2 := combine(expand(evalc(Re(l15))), trig):

l3 := combine(expand(evalc(Im(l15))), trig): v[0] := 1; 1

fsolve({l1, l11, l12, l13, l14}, {beta[n], gamma[n], gamma[2*n], gamma[3*n], gamma[4*n]}):

fsolve({l11, l12, l13, l14, l2}):

solve({l11, l12, l13, l14, l3}):

thanks

Reyhaneh

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