Try adding one of the following to the end of the DSolve line:
//ComplexExpand//Simplify
OR
//ComplexExpand//FullSimplify
Unfortunately, even this doesn't always work.At that point,you have 4 options (that I can think of, anyway):
1) Solve the problem numerically using NDSolve (probably the best idea, if you can get enough accuracy).
2) Plot the graph anyway (it will just have some blank spots in it)
3) Assume the imaginary part is ignorable and take the Real part of your answer (using the Re function). To be honest,since I'm not entirely sure howMathematica's algorithms work for diff equations, I would be a little hesitant to do this without knowing a bit more. (Notice that this is really a fancier version of option 2.)
4) Use some other method to solve the problem symbolically (i.e., solve the characteristic polynomial numerically, then use what you know about the form of the homogeneous solution and the particular solution). This is probably the best way, but it can be a lot of extra work (and probably won't get you much extra payoff). I would save this for when you are going to do some serious work with that particular diff. equation.