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Take real numbers

k = 9.; l = 12.; m = 2.; M = 4.;
mat = {{m*w^2 - 2*k, k, k*Exp[-3 I*ka]k*zeta}, {k, M*w^2 - (l + k), 
l}, {-k*Exp[-3 I*ka]k*zeta, l, M*w^2 - (k - l)}};
mydet = ExpToTrig[Det[mat]];
sol = Quiet@Solve[mydet == 0, w];
funcs = wChop[w /. sol /. {zeta -> Exp[-3I ka]} // FullSimplify;FullSimplify];

Use for the real part

Plot[1/2Show[Table[Plot[Max[0, Flatten[funcs(funcs[[k]] + Conjugate[funcs]]Conjugate[funcs[[k]]])/2], {ka, 0, \[Pi]}, PlotStyle -> Black], {k, 1, Length[funcs]}], PlotRange -> All]

and

Plot[1/2Show[Table[Plot[Max[0, Flatten[(funcsfuncs[[k]] - Conjugate[funcs]Conjugate[funcs[[k]]])/I](2 I)], {ka, 
 0, \[Pi]}, PlotStyle -> Blue], {k, 1, Length[funcs]}], PlotRange -> All]

for the imaginary part.enter image description here

enter image description here

Take real numbers

k = 9.; l = 12.; m = 2.; M = 4.;
mat = {{m*w^2 - 2*k, k, k*Exp[-3 I*ka]}, {k, M*w^2 - (l + k), 
l}, {-k*Exp[-3 I*ka], l, M*w^2 - (k - l)}};
mydet = ExpToTrig[Det[mat]];
sol = Quiet@Solve[mydet == 0, w];
funcs = w /. sol // FullSimplify;

Use for the real part

Plot[1/2 Flatten[funcs + Conjugate[funcs]], {ka, 0, \[Pi]}]

and

Plot[1/2 Flatten[(funcs - Conjugate[funcs])/I], {ka, 0, \[Pi]}]

for the imaginary part.

Take real numbers

k = 9.; l = 12.; m = 2.; M = 4.;
mat = {{m*w^2 - 2*k, k, k*zeta}, {k, M*w^2 - (l + k), 
l}, {-k*zeta, l, M*w^2 - (k - l)}};
mydet = ExpToTrig[Det[mat]];
sol = Quiet@Solve[mydet == 0, w];
funcs = Chop[w /. sol /. {zeta -> Exp[-3I ka]} // FullSimplify];
Show[Table[Plot[Max[0, (funcs[[k]] + Conjugate[funcs[[k]]])/2], {ka, 0, \[Pi]}, PlotStyle -> Black], {k, 1, Length[funcs]}], PlotRange -> All]
Show[Table[Plot[Max[0, (funcs[[k]] - Conjugate[funcs[[k]]])/(2 I)], {ka, 
 0, \[Pi]}, PlotStyle -> Blue], {k, 1, Length[funcs]}], PlotRange -> All]

enter image description here

enter image description here

Post Deleted by Cesareo
Source Link
Cesareo
Cesareo
  • 4k
  • 8
  • 12

Take real numbers

k = 9.; l = 12.; m = 2.; M = 4.;
mat = {{m*w^2 - 2*k, k, k*Exp[-3 I*ka]}, {k, M*w^2 - (l + k), 
l}, {-k*Exp[-3 I*ka], l, M*w^2 - (k - l)}};
mydet = ExpToTrig[Det[mat]];
sol = Quiet@Solve[mydet == 0, w];
funcs = w /. sol // FullSimplify;

Use for the real part

Plot[1/2 Flatten[funcs + Conjugate[funcs]], {ka, 0, \[Pi]}]

and

Plot[1/2 Flatten[(funcs - Conjugate[funcs])/I], {ka, 0, \[Pi]}]

for the imaginary part.