What are the requirements for a 'complex' airplane?
For the FAA, a "complex aeroplane" must have:


A retractable gear (not necessary for a seaplane);
In-flight adjustable flaps; and
A controllable pitch propeller.


The FAA's definition is given in 14 CFR 61.1:


  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.


However, the EASA has a different definition of a "complex motor-powered aircraft" that is an airplane, which is considerably more "complex":


  an aeroplane:
  
  
  with a maximum certificated take-off mass exceeding 5 700 kg, or
  certificated for a maximum passenger seating configuration of more than nineteen, or
  certificated for operation with a minimum crew of at least two pilots, or
  equipped with (a) turbojet engine(s) or more than one turboprop engine
  


Note that 5700kg is about 12567 pounds.