  We show that the Khovanov complex of a rational tangle has a very simple
representative whose backbone of non-zero morphisms forms a zig-zag.
Furthermore, this minimal complex can be computed quickly by an inductive
algorithm. (For example, we calculate $Kh(8_2)$ by hand.) We find that the
bigradings of the subobjects in these minimal complexes can be described by
matrix actions, which after a change of basis is the reduced Burau
representation of $B_3$.
