ΔE 31.5, loose: different enough that you should pick on purpose. Imperial Purple is noticeably darker, much more saturated than Deep Violet.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 31). Imperial Purple is noticeably darker, much more saturated than Deep Violet.
The same difference applies the other way round: Deep Violet is noticeably lighter, much more muted.
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 Deep Violet on the colour wheel See Imperial Purple on the colour wheel
All matches: Deep Violet equivalents · Imperial Purple equivalents