I am meant to "sketch" the set $|z - 1 + i| \leq 3$ for my Complex Analysis homework. I am able to draw this set by hand, so my question isn't about that! Rather, I would like to know how a professional mathematician would generate such an image if he or she were submitting the image as part of a journal article. What program/software/code would he or she use?...all I need is a direction to head in!
(For context: I get extra credit in the class for submitting my homework typed out in Latex. And for this question, I'm sure I could just leave a blank space and hand draw the diagram. I also found this answer, which is kind of a hacker way to generate such diagrams. But my aspiration is to become a mathematician, and so I wanna know how a real mathematician would make such a diagram! Thanks in advance!)
Another tool that can be incorporated into LaTeX documents: Asymptote. It's a programming language, so there's a learning curve there. On the plus side, it comes standard with TeX distributions, and the usual editors can easily be configured to run Asymptote code in the same .tex file as everything else.
Drawing circles is in the base capabilities of Asymptote even before importing any of the standard libraries.