§ 61.1(b)
Complex airplane means an airplane that has a retractable landing gear, flaps, and a controllable pitch propeller, including airplanes equipped with an engine control system consisting of a digital computer and associated accessories for controlling the engine and propeller, such as a full authority digital engine control; or, in the case of a seaplane, flaps and a controllable pitch propeller, including seaplanes equipped with an engine control system consisting of a digital computer and associated accessories for controlling the engine and propeller, such as a full authority digital engine control.
The FADEC inclusion is for planes like Cirruses (Cirri?) that the FADEC controls the CS prop. You aren’t doing anything, but it still counts. Obviously, Cirrus aircraft aren’t retractable, so they still don’t count as complex.