When I say "simple" and "complex", the supercharger is just a blower, cooling lines, and a belt, for the most part. Sure there are lots of "little things" which also have to be added/changed, but the basic setup is simple. The turbo requires a lot more "little things" as it attaches to the exhaust, the piping for cooling, oil lines, plus other "little things" which must be added/changed. The basic setup is more complex because more things must be changed. Once you try to go into big setups for hp, the turbo is simple as the only thing which really needs to be changed is the turbo and tuning. The supercharger is only more complex when trying to compete with the turbo setup.
Not trying to start a debate on this. Just clarifying what I mean when I use these terms.