I have come across the phrase I will do used as a response. Somehow, it seems incomplete. Shouldn't it be I will do that?
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The reply I will do is to me less common than the other possibilities I will and I will do so, but perfectly normal. I will do that (in this sense) is even less likely, but still possible.
I will do might be a response to Will you do that? in which case I will do that is a more usual response. However I will do could also be a response to the question Who is good enough for the job?, in which case it means I am good enough.