It means to come and see. I am wondering why not using te form in this particular phrase?
Is this correct? If so, how is it different from the one above?
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Yes the sentence with 見に来る is correct. に particle has different uses and amongst that, there is one use, wherein the person goes somewhere to do something.
The form is like Vmasu Form of Verb + に + place (can be before the verb) + に(if the place is used after the usage of the verb) + verb of motion. E.g. 見る verb's masu form is 見ます, so 見にxyzに来る, I will come to watch/see.
Here in your sentence, the place is not in between, that means it is either implied by the sentence or is placed before the verb of action.
Also, please note that, this usage of に only applies with the verb of motion as the 2nd verb, and for what verb you are going to perform can be any, i.e. Masu form of Any verb+ に + Place + MOTION VERB (it will mean going/coming etc etc. for/to do eat/drink etc. etc.)
2. Coming to 見て来る. て form, has among other things is used as conjunction i.e. "and". So, over here it can mean, watch and come.
There is another くる and this one is usually written in hiragana. It has some other meaning. I will not be able to explain this use, when くる e.g. is used as an auxiliary(still learning this one). In this one hiragana will be used, so that you might be able to differentiate e.g. 見てくる will be used rather than 見て来る. To give the くる an auxiliary meaning
Hope it helps !
For the 見に来る I have used, A dictionary of basic Japanese Grammar as a reference.