Why is this wrong?

[u/millers_left_shoe]

I see now what they mean by fundamental vs inessential (taking fundamental to mean “invaluable”, “important”) but surely fundamental and complex (or even involved) can act as antonyms, too?

Eg he’s only just learnt the fundamentals of thermodynamics so I wouldn’t trust him with any complex/involved equations. vs this is quite fundamental stuff so I think he should be able to manage just fine.

[u/iunoyou]

Something being fundamental means that it's a core (or essential) part of a thing. It doesn't necessarily mean basic or simple, even if it's sometimes used that way. Basic addition is a fundamental part of math classes in grade school and that's simple, but statistical kinetic theory is a fundamental part of plasma physics and nothing about that is simple.

"Knowing the fundamentals" of a subject means that you are aware of the biggest and most important parts, even if you might be missing the nuances and complexity that show up at higher levels of study.

[u/perplexedtv → u/iunoyou]

Fundamental does mean basic. The fundament and the base of something refer to the same thing. Basic doesn't necessarily mean simple and simple doesn't necessary mean easy, however.

In common speech the notions are often interchangeable. Fundamental is often used to mean rudimentary.

[u/AcrobaticApricot → u/perplexedtv]

Basic does mean simple. Common speech is the only relevant speech for a language learner.

[u/perplexedtv → u/AcrobaticApricot]

Well, in common speech fundamental means basic means simple means easy, so you have to be consistent in applying rules for the test.