File talk:ExpIm.png

Is it possible to amend the axes so as to, for example, make the Y axis multiples of pi? 0-5-10-15 is less meaningful than 0-pi-2pi-3pi etc. would be.

Similarly, the x axis would be more meaningful if it were a log axis.

Finally, an indication of what the gradients were may also add meaning. --prime mover (talk) 11:34, 3 January 2017 (EST)

Yes I can do that; what do you mean by an indication of the gradients, other than the color scale on the right side? --GFauxPas (talk) 12:45, 3 January 2017 (EST)

There's no indication of what the value of the function is at the gradients themselves. --prime mover (talk) 15:47, 3 January 2017 (EST)

The legend shows that you have that the darkest red is around $-20,000$ and the darkest blue is around $+20,000$. Are you saying I should impose numbers on the graph itself? --GFauxPas (talk) 18:17, 3 January 2017 (EST)

There are black lines on the graph. What, for example, is the value of Im(e^z) for, say, the leftmost black arc on each row, and thence the increment in Im(e^z) for the next arcs to the right? A legend, for example, saying "Gradient lines are at every $n$" or whatever. Graphical presentation 101. --prime mover (talk) 18:36, 3 January 2017 (EST)

Makes sense. So you're saying I should graph $\operatorname{Im}(f(\ln x + iy))$, in effect? --GFauxPas (talk) 16:28, 4 January 2017 (EST)

Am I? I don't know, all I know is that I don't know what those black lines mean on your graph. --prime mover (talk) 17:15, 4 January 2017 (EST)

yes I know I'm taking care of that. I'm asking about your suggestion that I should use a log axis. Doesn't using a log axis on an exponential function kind of defeat the point of the graph? --GFauxPas (talk) 17:41, 4 January 2017 (EST)

Don't know what the point of the graph actually is -- the interesting thing about the exponential function is that the value is sinusoidal with increase of imaginary, and that doesn't come out well here. And it doesn't show the "whole" plane anyway, so you don't know what happens for negative reals.

But never mind. Not my game. --prime mover (talk) 17:56, 4 January 2017 (EST)

Hm, maybe you're right. I'll think about it. What about graphs of the images of a set of contours? Say, of contours holding $x$ constant, $y$ constant, $r$ constant, and $\theta$ constant? --GFauxPas (talk) 13:14, 5 January 2017 (EST)

Image of a grid? Diagram 1: draw the grid formed by $x = \ldots, -3, -2, -1, 0, 1, 2, 3, \ldots$ and $y = \ldots -3i, -2i, -i, 0, i, 2i, 3i, \ldots$ and on the Diagram 2: the lines formed by the images of these lines. --prime mover (talk) 13:28, 5 January 2017 (EST)

Yes exactly. And likewise for $r = 0, 1, 2, 3, \ldots$ and $\theta = \left({-\pi..\pi}\right]$. Would that be interesting? --GFauxPas (talk) 13:32, 5 January 2017 (EST)