# How to solve a symbolic complex equation with real and imaginary parts?

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Nélio Dias on 6 Apr 2021
Commented: Nélio Dias on 7 Apr 2021
I have to solve this polynomium: to . So, I know that to solve this equation I have to replace the s to get Therefore, the real and imaginary parts will be zero and we have and So, to solve this in matlab, I write this code:
syms s k w
den = s^3 + 9*s^2 + 14*s + 126
assume([ k> 0,w >0])
solw = solve(imag(den)==0, w)
den = subs(den, w, solw)
solk = solve(den==0, k)
Then, this code work well, but if I change the polynomial degree I will have to change the parameters of solve function. So I to know if there is a more generic way to solve this equations

Paul on 7 Apr 2021
I'm not sure what "change the paramters of the solve function" means. If a general apprach is desired, maybe something along the lines of simultaneously solving two equations for two unkonwns:
>> syms s w k
assume(w>=0); assume(k>=0);
D(s) = s^3 + 9*s^2 + 14*s + 2*k;
eqn = [real(D(1j*w))==0, imag(D(1j*w))==0];
sol = solve(eqn,[w k],'ReturnConditions',true);
[sol.w sol.k]
ans =
[ 0, 0]
[ 14^(1/2), 63]
Change D(s) as desired.
Nélio Dias on 7 Apr 2021
Thanks for you comment, Walter