Im curious about how to plot sets of $\Bbb R^2$ or $\Bbb C$ in some computer algebra systems, mainly sage, axiom, mathematica and maple, by order of preference.
To make the question not too broad it is enough for me just one example. How you can plot a set like
$$\{z\in\Bbb C: |z-3|<|z+2i|\}$$
in the above mentioned CAS. My interest is mainly sage and axiom, the other systems I put here optionally.
Note: the above set was typed randomly. It is just an example to see how I can write the code. Thank you in advance!
In Mathematica, use ImplicitPlot or RegionPlot. You might have to first convert complex numbers into $(x,y)$ coordinates.
But you don't need a CAS for your specific example. Your set is $$ \big\{(x,y) \in \mathbb{R}^2: (x-3)^2 + y^2 < x^2 + (y+2)^2 \big\} $$ The quadratic terms all disappear, so this simplifies into something that's easy to plot by hand. Or, thinking more geometrically, consider the set of points that are closer to $(3,0)$ than to $(0,-2)$.