4 years, 10 days

## How to plot conformal map...

Maple 2020

Hello!

I just want to try plot a conformal map for better understanding how it works.

For example, I want to plot a conformal map, so I do this:

restart;
assume(y, real);
assume(x, real);
f := z -> I + z*exp(1/4*I*Pi);
w := f(x + y*I);
u := Re(w);
v := Im(w);
A := array(1 .. 2);
A[1] := plots:-conformal(z, z = 0 .. 1 + I/2, grid = [16, 16], numxy = [16, 16], scaling = constrained);
A[2] := plots:-conformal(f(z), z = 0 .. 1 + I/2, grid = [16, 16], numxy = [16, 16], scaling = constrained);
plots:-display(A);

It works fine. But if I want to map more complecated region, I have lot's of problem. Could you help me please.

For example:

how to map a triangle [0,0], [1,0], [0,i] or half-plane Im z> 1, excluding the circle | z - 2i | <= 1.

Thank you!

## Plot complex region...

Maple

Hello!

I just want to plot a complex region:

abs(z - 1) > 1

abs(z + 1) > 1

Im(z) > 0

In Mathemactica it's really easy (ComplexRegionPlot[
Abs[z - 1] > 1 && Abs[z + 1] > 1 && Im[z] > 0, {z, -5 - 5 I,
5 + 5 I}])

But I like Maple and I want to use it. Could you help me please...

This way that I can found here not working:

ineq1 := 1 < abs(z - 1);
ineq2 := 1 < abs(z + 1);
ineq3 := 0 < Im(z);
plots[implicitplot]([eval(ineq1, z = x + y*I), eval(ineq2, z = x + y*I), eval(ineq3, z = x + y*I)], x = -10 .. 10, y = -10 .. 10, gridrefine = 3, scaling = constrained);

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