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Instead of thinking of real analysis as a zoo of weird exceptions, it's probably more accurate to think of complex analyic functions as the exceptions. For exam
by curt15 2y ago
Instead of thinking of real analysis as a zoo of weird exceptions, it's probably more accurate to think of complex analyic functions as the exceptions. For example, when viewed as a two dimensional mapping from the plane to itself, complex-analytic functions are conformal (angle-preserving) whereas most differentiable mappings from the plane to itself are not.
- dhosek 2y agoOn the other hand, complex analysis explains things that aren’t obvious in real analysis, like why the radius of convergence for a continuous function on the real line might be 1 (turns out there are singularities off the real line on the complex plane).