Good job on this one! As a former mathematics student, I really loved the use of set notation in the instructions, as well as the distinction between stats in each world being represented by real and imaginary numbers, respectively. I also thought having to switch between worlds to shoot enemies was neat.
Something I thought was a little confusing, though, was why I didn't have to eliminate all of the enemies in order to progress; being taken to the upgrade screen the Also, there didn't seem to be any indication that enemies were being hit; I think a recoil animation of some kind might do the trick.
Still, I love the concept, thought the music was fitting, and had a good time overall. Great work!