It depends on how strong the purple dye is and how black the current black is.
I would say the most likely is that you will not see the purple at all.
Where did you buy the purple and black dye? Is it from Hot Topic or a pharmacy, or is it from a specialty store for colorists, like Sally Beauty Supply? Hot Topic dyes are notoriously weak.
Here is a semi permanant dye in dark purple, however, if your hair is a light color it will not go on dark purple. if you have light hair I would suggest darkening it to a deep brown before trying for the dark purple.