LogPlot. Without Log, there is no problem. But when I try to plot with Log

Hi,
I having hard time with LogPlot.

Please find the attach file.
Without Log, there is no problem. But when I try to plot with Log gives a lot of errors
I spen a lot of time to see why!!
I really apreciate your help
Regards
Jabir

The log of a negative number is an imaginary number. You can change the sign of the real parts that are negative as follows:

Eps1[\[Omega]_] := (p[\[Omega]][[1]]^2 - p[\[Omega]][[2]]^2) + 
   I*2*(p[\[Omega]][[1]]*p[\[Omega]][[2]]);
LogPlot[{-Re[Eps1[\[Omega]]], Im[Eps1[\[Omega]]]}, {\[Omega], 1, 5}, 
 PlotStyle -> Thick, PlotRange -> All]

Thank you very much. But this is did not solve the problem. For examble, if we plot just the imaginary part which gives real numbers , the problems still there.
Regards
Jabir

Thank you very much. But this is did not solve the problem. For examble, if we plot just the imaginary part which gives real numbers , the problems still there.
Regards
Jabir

But my plot shows AND RE and Im!?
Here is a plot of only the imaginary part (this is in fact a rescaled plot of the orange curve above). I do not see the problem…