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Why do functions in complex analysis behave so well? (as opposed to functions in real analysis)

Why is it that complex analysis seems to be so developed? What is it that makes complex numbers more interesting than, say, quaternions? (I am currently taking real analysis.)

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Meta thread at meta.mathoverflow.net/discussion/1276/… – Yemon Choi Jan 14 2012 at 7:52
This is not quite an exact duplicate of the question I indicated, but I think it is close enough to the first question. For the second question, it's hard to decide where one should start... – S. Carnahan♦ Jan 14 2012 at 8:12

closed as exact duplicate by Andres Caicedo, Dan Petersen, Will Jagy, GH, S. Carnahan♦ Jan 14 2012 at 8:09

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