Complexes are basically a collection of prepared and secured modules that have been specialised. This is needed to effectively control emplacements.
1 complex will effectively allow 100 hulls to run at 100% of its crew factors. Therefore a 1000 hull platform will require 10 complexes. Only the total hulls is used so two platforms of 50 and 150 hulls respectively will require 2 platforms.
Uncontrolled platforms, i.e. those without a controlling starbase or those linked to a starbase with no platform control complexes will have only 20% of their normal crew factors.
In all cases excess crew factors can compensate for lack of platform control complexes.