Should I say
I look forward to hearing from you
looking forward to hear from you?
I have doubt because I know that the form of a verb is "to+ infinity" without the addition of the -ing that changes it to become a noun.
This is a very common mistake!
So, don't worry. Here is the cure.
Ask yourself which one makes more sense: "look forward to it" or "look forward to do it"?
Chances are you know that "look forward to it" sounds more natural, because you've seen or you've heard others use it that way before. And, yes, with look forward to, you need hearing from you (NOT
hear from you).
The trick is to remember that to can be either the infinitive marker or a preposition1.
You need a verb after the infinitive marker to (e.g. I want to swim this evening).
You need a noun after a preposition (e.g. She went back to the pool.)
It doesn't have to be a real noun, just something that functions like a noun. In other words, it's the object of a preposition, as it's traditionally called; or as defined a little more precisely (same link):
The prepositional complement is typically a noun phrase, but it may also be a nominal relative clause or an -ing clause. Both the nominal relative clause and the -ing clause have a range of functions similar to that of a noun phrase: ...
In your example, to in look forward to is a preposition. Why? Because you can say look forward to something (e.g. He had worked hard and was looking forward to his retirement.) In other words, saying "I'm looking forward to it" makes sense.
And that makes you need a noun or something noun-like, i.e., hearing, not hear:
I look/'m looking forward to hearing from you.
1When the preposition to is used in a phrasal verb, some people call it a particle, but let's keep this post simple and use only the term "infinitive marker" and "preposition".) Here is a list of such phrasal verbs (ending with to). Some common ones, in my opinion, are look forward to and be used to. Another common phrasal verb (but not on that page) is object to.
Here is a related mistake which shares the same cause of confusion: used to vs. be used to.
Remembering this may be helpful:
He used to live in Frankfurt, but he's not used to living in cold weather.
The first to is the infinitive marker to. The second to is a preposition.
The first to is about "He used to do something".
The second to is about "He's not used to something".
"Look forward to" is a phrasal verb, in which "to" is a preposition; it is a part of the phrase, not the part of the infinitive hear. So it takes a noun or the -ing form of a verb, even you use the phrase in the progressive form. So your first sentence is OK grammatically, but the second one isn't. It should be:
I am looking forward to hearing from you.
I would use hearing on both.
Also the second example is not a question, but basically a shortened form of the first example. Definitely informal.
I look forward to hearing from you.
(I am) looking forward to hearing from you.
to is part of looking forward to (some action). Not the infinitive form of the verb.
The word “to” in this phrase is slightly confusing because it is usually used to introduce a verb, as in “want to” or “have to”. Even though saying “I want to hear from you” is completely correct, “to look forward to” employs a different pattern:
I look forward to [a thing you would like to happen]
Obviously, “hear” is not a thing, so it wouldn’t make much sense to “look forward to hear from you”. The thing you are looking forward to is “hearing from you”:
I look forward to hearing from you. (correct)
I look forward to hear from you. (wrong)
As for the question whether to use “I look forward to” or “I am looking forward to”, some people consider the two completely interchangeable, but most find the phrase with “look forward to” somewhat formal and best suited for formal correspondence, whereas “to be looking forward to” is more informal and friendly:
I look forward to hearing from you. (correct in formal writing)
I am looking forward to hearing from you. (correct in an informal context)