The sentence is: 인터넷으로 사지 뭐하러 여기에 와?
I would paraphrase this as: 인터넷으로 사면 여기 올 필요 없으니까 왜 오려고 해?
Is this right? i think the 지 has some sort of connecting function, like 고 or 서.. but i couldn't find which grammar topic this is.
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Yes, it is right.
1) 지 can be a coordinate conjunction, for instance, "but" (contrary).
나는 축구선수지, 농구선수는 아니다.
I am a football player, but not a basketball player.
2) 지 is ending represents intimacy
엄마, 아빠는 저녁 먹고 오겠지.
Mom, I guess that father will come after dinner.
@ In dictionary, I can not find an usage like the sentence in OP.
But it seems that in real situation, mixing of 1) and 2) is widely used :
A. 니가 학생이지, 교수냐 ? = 니가 교수니 ? 학생이지.
You have no such right, because you are a student.
B. 인터넷으로 사지 뭐하러 여기에 와? close acquaintanceship
[add] When I hear "인터넷으로 사지 뭐하러 여기에 와?", I am unpleasant. If I translate this in English, then "You are stupid. Internet is enough"
If I say to someone, not a friend, then I will say "인터넷으로 사면 되요" or "인터넷으로 사지, 여기까지 왔니 ?"