00:14:22 -!- calamari_ has joined. 01:46:25 -!- calamari- has joined. 01:55:51 -!- calamari_ has quit (Read error: 104 (Connection reset by peer)). 02:34:48 -!- calamari- has quit (Read error: 110 (Connection timed out)). 02:35:26 -!- calamari- has joined. 02:59:16 -!- calamari- has quit ("Leaving"). 03:17:12 -!- calamari_ has joined. 03:31:42 -!- calamari- has joined. 03:32:46 -!- calamari_ has quit (Read error: 104 (Connection reset by peer)). 06:39:13 -!- calamari- has left (?). 07:59:59 -!- clog has quit (ended). 08:00:00 -!- clog has joined. 19:55:28 ho-hum. 19:55:44 well, now I have the solution for my last-evening function. 19:55:52 congrats :) 19:56:10 considering that I got it from the course assistant, I don't think it warrants congratulations. 19:58:06 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 maybe 'u' was an unfortunate name. 20:00:18 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 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 phew. 20:01:55 mm