Solutions for the dispersion relation for waves propagating in the (x, y)-plane for two propagation directions (α = 0 solid line, and α = π/4 dashed line) with respect to the wavenumber, k. The density ratio is d = 0.5, the Alfvén speed of the lower plasma is v_A = 10 km s⁻¹, and the magnetic field inclination angle is θ = 5°. The upper panel shows the real part of the frequency, while the imaginary part is plotted in the lower panel. The limiting value of ℑ(ω) when k → ∞ is shown by the grey horizontal lines in the lower panel. For illustration we also show the real and imaginary part of the frequency in the case of a tangential discontinuity (θ = 0), plotted here in green.