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A complex airplane is defined by the United States, Federal Aviation Administration as an aircraft that has all of the following:
In the U.S., students generally train for their first pilot certificate in an aircraft with fixed landing gear and a fixed-pitch propeller. It may or may not be equipped with flaps.
Before or after earning the private pilot certificate (PPL) (usually after), a pilot can be trained in complex aircraft operation by a flight instructor. When the pilot has demonstrated proficiency in complex aircraft, the flight instructor endorses the pilot's logbook and the pilot is said to have a "complex endorsement".
The FAA requires a pilot to have experience in, and take at least part of the practical test in, a complex airplane in order to earn the commercial pilot certificate (CPL) and the flight instructor certificate (CFI).