"낚시하는 남자가 누구인지 압니까?"
Translation:Do you know who the fishing man is?
I would rather leave it to the experts to explain this but from what I have gathered so far:
인 comes from 인다 meaning am/is/are - present tense of 이다, in neutral style.
(i) -지: a noun modifier particle, similar to -것 / -거. They are added to the conjugated verb base/stem of a clause to transform the clause into a noun form. #nominalisation.
This process would enable this clause to be linked to another clause.
An example in English would be:
"When the going gets tough, the tough get going",
where go (verb) and tough (adjective) are made into nouns, the going, the tough) to act as subjects.
-지 is used instead -것/-거 to nominalize clauses which are in the form of questions, enquiries i.e. clauses with who? what? which? where? when? whether/if? etc.
(1) Main clause: [Subordinate clause]-지 압니까? = Do you know [...] ?
(2) Subordinate clause: 낚시하는 남자가 누구 인(다) = who the fishing man is
(3) On putting the 2 clauses together to form a sentence, the 다 in the subordinate clause drops off,
[낚시하는 남자가 누구 인]-지 압니까? = Do you know who the fishing man is?
In short, 인지 --> 인 = is (which belongs to the Subordinate clause; while 지 is the link particle joining the 2 clauses.
Fishing before man qualifies it. He's the sort of man who goes fishing, probably what we'd loosely call a fisherman. Fishing after man modifies it. He's a man who's doing something to do with fishing. Surely this should be, "Do you know who the man fishing is?" Fisherman seems to be 어부, fishing man 낚시꾼 at least in the dictionaries.