The most common and most likely answer to this crossword clue is the 11 letter word ELABORATION
I've seen this crossword clue in The Times
E
L
A
B
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A
T
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Buddy explains!
The straight part
We know that "Complexity" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case complexity = elaboration.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does ELABORATION mean?
ELABORATION noun- The act or process of producing or refining with labor; improvement by successive operations; refinement.
- The natural process of formation or assimilation, performed by the living organs in animals and vegetables, by which a crude substance is changed into something of a higher order
- Setting up a hierarchy of calculated constants in a language such as Ada so that the values of one or more of them determine others further down in the hierarchy.
- The process of taking a parsed tree of an abstract integrated circuit definition in a language such as Verilog and creating a hierarchy of module instances that ends with primitive (atomic) gates and statements.
- (psychology) The level of processing of a message or argument.