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19:55:28 <fizzie> ho-hum.
19:55:44 <fizzie> well, now I have the solution for my last-evening function.
19:55:52 <lindi-> congrats :)
19:56:10 <fizzie> considering that I got it from the course assistant, I don't think it warrants congratulations.
19:58:06 <fizzie> the official way to solve it was to look at the function "u(z) = f(z) + z^3 - 3z", which is analytic and differentiable everywhere f(z) is, and that particular function makes f(z) simplify a bit, so that it is possible for a normal human to just look at lim_h->0 (u(z+h)-u(z))/h.
19:58:31 <fizzie> maybe 'u' was an unfortunate name.
20:00:18 <fizzie> and apparently also if the component functions u(z) and v(z) (when f(z) = u(z)+iv(z)) are differentiable and satisfy the cauchy-riemann equations in a single point, the function is indeed complex-differentiable there. it is a sufficient condition, but we weren't quite sure if it's a necessary one, too.
20:01:06 <fizzie> if the latter, it can be used to show that f(z) is complex-differentiable on the coordinate axes and analytic nowhere.
20:01:09 <fizzie> phew.
20:01:55 <lindi-> mm