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The phrase "a complex set" is correct and usable in written English.
It can be used to describe a group of items, ideas, or elements that are intricate or multifaceted in nature.
Example: "The researchers analyzed a complex set of variables that influenced the outcome of the experiment."
Alternatives: "a complicated collection" or "an intricate group".
Exact(58)
The Internet presents educators with a complex set of problems.
It's also quite a complex set of subduction zones.
Clearly, this is a complex set of issues that yields no simple answers.
But there's a complex set of interests at work here and only so much money".
"We face a complex set of economic, social and political challenges.
A complex set of political calculations appears to be behind Reid's decision.
Each of these is a complex set of issues in its own right.
As I found out, there is quite a complex set of rules associated with that carpet.
"It's such a complex set of relationships," the State Department official said.
"This was a complex set of circumstances involving a number of people.
It was a complex set of proposals, which were not readily understood.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com