The most common and most likely answer to this crossword clue is the 15 letter word REPRESENTATIONS
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More clues leading to the result REPRESENTATIONS
Buddy explains!

The straight part
We know that "Complaints" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case complaints = representations.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 REPRESENTATIONS mean?
REPRESENTATIONS noun- That which represents something else.
- The act of representing.
- The lawyers and staff who argue on behalf of another in court.
- The ability to elect a representative to speak on one's behalf in government; the role of this representative in government.
- An object that describes an abstract group in terms of linear transformations of vector spaces; (more formally) a homomorphism from a group on a vector space to the general linear group (group of all bijective linear transformations) on the space.
- A figure, image or idea that substitutes reality.
- A theatrical performance.
- Formal statements made to an authority to express discontent.