ΔE 30.5, loose: different enough that you should pick on purpose. Imperial Purple is a little darker, much more saturated, warmer than Sorcerer's Cloak.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 31). Imperial Purple is a little darker, much more saturated, warmer than Sorcerer's Cloak.
The same difference applies the other way round: Sorcerer's Cloak is a little lighter, much more muted, cooler.
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 Sorcerer's Cloak on the colour wheel See Imperial Purple on the colour wheel
All matches: Sorcerer's Cloak equivalents · Imperial Purple equivalents