How to plot |z-1| = 2 in a specified domain in Mathematica?

Question

How do I plot |z-1| = 2, from -10 to +10 in the real line and from -10i to +10i on the complex line? I've been trying for ages and seems like I can't get it right. Z stands for a complex number!

Also, could I use as well the x+iy notation in mathematica? or a+ib?

Thanks

Answer 1

For a contour plot:

ContourPlot[Abs[x + I y] == 2, {x, -10, 10}, {y, -10, 10}]

To just plot a (real-valued) function:

Plot3D[Abs[x + I y], {x, -10, 10}, {y, -10, 10}]

Choice of variable names is, of course, completely arbitrary.

Just for fun: with some smart choices, you can plot a complex-valued complex function, for example by piecing together Plot3D or ContourPlot3D with Animate.