The words complex and complicated have similar meanings, but their usage has some nuances.
Complex refers to something made up of many different parts that are intricately connected or related. These parts often work together in an intricate or sophisticated manner. Due to the number of interconnected factors or relationships involved, something complex may be difficult to understand or decipher. For example, a complex machine might have many intricate parts that work together to perform a specific function.
On the other hand, Complicated suggests something difficult to understand, follow, or execute due to having many parts, stages, or factors that are hard to keep track of or manage. It often implies difficulty or complexity that may be unnecessary or excessive. For instance, a complicated set of instructions might be complex because there are too many steps or they are not presented clearly.
In summary, while both words convey a sense of many interconnected parts or factors, complex emphasizes the intricate relationships between those parts, often suggesting an inherent sophistication. Complicated focuses more on the potential difficulty or challenge posed by the number of parts or steps involved.