ΔE 16.7, loose: different enough that you should pick on purpose. Imperial Blue is much more saturated, cooler than Amethyst Rayne.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 17). Imperial Blue is much more saturated, cooler than Amethyst Rayne.
The same difference applies the other way round: Amethyst Rayne is much more muted, warmer.
ΔE is the colour difference between our two swatch estimates: under about 6 is close, over about 15 is loose. Real paints also differ in finish, coverage and how they thin, so test before you commit.
See Amethyst Rayne on the colour wheel See Imperial Blue on the colour wheel
All matches: Amethyst Rayne equivalents · Imperial Blue equivalents