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I need to write a function f1 and f2 such that g(z) = 1/z and f1(g(z)), f2(g(z)); both plots on the same graph should look something like this graph: http://i.stack.imgur.com/iWDrk.png

So far i came up with:

f1 := z -> -Im(z);
f2 := z -> -Re(z);
g := z -> 1/z;

h := plot(f1(g(z)), z = -6 .. 6, y = -6 .. 6);
g := plot(f2(g(z)), z = -6 .. 6, y = -6 .. 6);
display({h, g});

Which shows a completely different graph.

edit: f1 (horizontal lines) and f2 (vertical lines) both contourplots should look similar to this: http://i.stack.imgur.com/pkLxM.png

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What about functions $f_1$ and $f_2$ is known? – M. Strochyk Oct 9 '12 at 6:02
hint: look at the maple help-page for plots[conformal] and figure out what the lines (2nd example, for 1/z) mean. Can you produce something similar with, say, a sequence of calls to plots[complexplot] to map grid lines? – acer Oct 9 '12 at 9:11
@M.Strochyk, f1 (horizontal lines) and f2 (vertical lines) both contourplots should look similar to this: i.stack.imgur.com/pkLxM.png – hagen1339 Oct 9 '12 at 11:59
@acer, Is it possible to do this with both f1 and f2 as contourplot and then plot f1(g(z)), f2(g(z))? – hagen1339 Oct 9 '12 at 12:02

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