How is a complex high power rocket defined?

A complex high power rocket is defined as one having more than one stage or a cluster of motors because this definition captures the intricacies and advanced design elements required for such rockets. Multi-stage rockets utilize a series of stages that are designed to drop off as they consume their fuel, allowing the remaining stages to continue carrying the payload to greater altitudes. This multi-stage design adds complexity to the rocket's mechanics, flight behavior, and recovery systems, demanding a higher level of skill and understanding from the rocket builder in terms of aerodynamics and propulsion.

Similarly, a cluster of motors can significantly enhance a rocket's thrust and provide redundancy, which necessitates careful planning and execution in the design and construction processes. These factors contribute to the rocket being classified as complex, as they involve advanced engineering principles that extend beyond those required for simpler designs, such as single-motor configurations.

The other definitions do not encompass the full scope of what makes a high power rocket complex. Single motor setups, weight alone, or basic recovery devices do not involve the advanced engineering considerations inherent in designing a rocket with multiple stages or clustered motors.