Langmuir waves dispersion relation

[ian2012]

I was just looking at an expression (a dispersion relation, omega^2 = ...) similar to that of warm electron's in a plasma http://en.wikipedia.org/wiki/Plasma_oscillation expect with an extra imaginary term, which I think comes out from the full derivation of the dispersion relation for warm electrons. I am guessing the relation that everybody knows of is then the Real part of the expression I was looking at.
My question is, can a purely imaginary term have some physical significance? Surely it isn't physical?

 

[Feldoh]

Typically imaginary numbers deal with phases

 

[PhilDSP]

Mathematically, you can split a single-valued wave of arbitrary phase for each frequency component it contains into 2 components where the difference in phase of each frequency is 90 degrees. The more phase advanced of the 2 is called real while the least advanced is called imaginary. Both are necessary to reconstruct the original wave.