Question

How do you sketch the set of all the complex numbers z such that `|z- 3- 4i| = 2`?

Answer 1

This will be a circle of radius `2` centred on `3+4i`

Explanation:

graph{((x-3)^2+(y-4)^2 - 4)((x-3)^2+(y-4)^2-0.003) = 0 [-9.5, 10.5, -1.36, 8.64]}

If `z_1` and `z_2` are Complex numbers, then `abs(z_1-z_2)` is the distance between `z_1` and `z_2`.

So we can read `abs(z-3-4i) = 2` as "the distance between `z` and `3+4i` is `2`".