Complex analysis has a lot of nice theorems that real analysis doesn't have: if you can take the complex derivative once, you can take it [tex]\infty[/tex] many times. Maximum modulus theorem; inside the radius of convergence the Taylor series of a function converges to the function.(adsbygoogle = window.adsbygoogle || []).push({});

So what I wonder is, is the elegance of complex analysis related to the fact that the complex #'s are algebraically complete?

Complex analysis can be used to show that the complex #'s are algebraically complete. So one could ask if that same proof works over other fields that are both metrically complete and algebraically complete. To try and get a handle on the question.

Laura

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# Elegant complex analysis

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