I haven't worked very much with recurrence relations, but for the ones I have worked with I always get real solutions, which is strange to me because looking briefly at the procedure for solving (linear) recurrence relations, it seems that we try to "find the roots that fit the polynomial". Why should this necessarily give real solutions, or is that just what intro discrete math books do- choose the coefficients to the recurrence relations to yield real solutions?
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2The problems are chosen to have real solutions. It is not too uncommon for students using these books to have little or no exposure to complex numbers (at least in the U.S.). – Brian M. Scott Jan 25 '15 at 22:41
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I see. And I just realized I have no idea what I put that in quotes, that's an entirely regular thing to do. – Jan 25 '15 at 22:43
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In some cases one can get a pair of nonreal complex conjugate roots, and use a term of the type $A \sin (kn)+B\cos(kn)$ to get the thing to give real results. – coffeemath Jan 25 '15 at 22:58
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Suggest you construct some of your own problems, linear degree two recurrence relations, see what happens when getting complex roots under various circumstances, different sizes of coefficients. – Will Jagy Jan 25 '15 at 23:53