These adjectives refer to something having interconnected parts which make the whole thing difficult to follow.

Complex suggests a combination of many associated parts.

Ex – They had made such a complex system that it was difficult to submit a simple form. Commonly used with system, structure, mixture, relationship, issue

Complicated stresses elaborate relationship between the parts.

Ex – Rubik’s Cube is a complicated puzzle. Commonly used with  problem, puzzle, relationship

Intricate refers to tangled parts.

Ex – The woman weaved an intricate pattern with the wool. Commonly used with design, pattern, carving, detail, melody

Convoluted is different as it means twisted and thus difficult to follow.

Ex – The plot of the movie was convoluted.

Commonly used with story, plot, scheme, argument, logic

 

 

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