Yay. Turns out if you assume \partial_\theta v = 0 for an analytic function, that function is going to be the complex log, up to assorted constants. Or so I think. Neat. One more problem solved, then. Only thirty or so more to go for this section...

Also, for some reason I've forgotten why the hell the triangle inequality for the real numbers works. This is, sadly, rather inconvinient *cough*, as it's used ALL THE DAMN TIME in the anal-retentive construction of the real number system that my analysis text is doing. It also makes me feel like a complete retard. And all the online 'proofs' of the triangle inequality that I've found focus on vectors and/or complex numbers, not the real numbers. And I know it should be trivial to get the real proof from the complex one, say. As I said, this makes me feel retarded.

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