The term complicated comes from watch nomenclature
. Each function of a watch is called a complication, so a watch with hours, minutes and seconds would have three complications, a watch with that plus day, date, and phase of the moon
would have six, and so on. A watch is usually referred to as complicated if it has more than the three basic functions.
Since watches were (and in many cases, still are) the most complex devices the average person comes in contact with, the term came to mean any complex device or situation.
This is not the only example of watches influencing language. Since they were the first miniaturized mechanical devices, other small mechanisms were often described as "watchworks" or "clockworks". Another word inspired by the watch is the use of the word "caliber" to designate quality (it refers to the size of the movement.)