Complex motion means it is not motion to calculate considering a single motion like linear motion, oscillatory motion, vibratory motion, rotatory motion and simple harmonic motion. Because they are combination of more than one type of motions.
Example: If we consider a particle of a vehicle’s wheel it undergoes rotatory motion with respect to the axle and it follows the path (road) with respect to the starting position. So if we like to study the motion of the particle with respect to the starting position we should consider it’s rotatory and motion on the path which is complicated called the complex motion.