The most common and most likely answer to this crossword clue is the 9 letter word LOVE-HATE
I've seen this crossword clue in The Guardian
L
O
V
E
-
H
A
T
E
Buddy explains!
The straight part
We know that "Complicated kind of relationship" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case complicated kind of relationship = love-hate.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 LOVE-HATE mean?
LOVE-HATE verb- To feel both love and hate (for someone or something), often simultaneously.
- (originally psychoanalysis) Of a relationship: involving feelings of both love and hate, often simultaneously.