Upper panels: ω_R/ω_k as a function of the normalized shear flow velocity, ΔU/c_A,0, for k_za = 0.1, m = 1, and three different collision frequencies (a) ν_ni/ω_k = 0.1; b) ν_ni/ω_k = 1 and c) ν_ni/ω_k = 10). Lower panels: ω_I/ω_k as a function of ΔU/c_A,0 for the same set of parameters as above. The red symbols represent the solutions of the full dispersion relation, i.e., Eq. (23); the blue solid lines correspond to the analytical approximation given by Eq. (30), and the blue dashed lines show the unstable branch of the neutral fluid when there is no coupling (Eq. (26)).