ΔE 17.9, loose: different enough that you should pick on purpose. Blue Violet is much more saturated, cooler than Imperial Purple.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 18). Blue Violet is much more saturated, cooler than Imperial Purple.
The same difference applies the other way round: Imperial Purple 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 Imperial Purple on the colour wheel See Blue Violet on the colour wheel
All matches: Imperial Purple equivalents · Blue Violet equivalents