What kind of graph is (|z| < 3) - (|z| < 1)?

[ahat]

help appreciated

[Jayward]

an annulus (doughnut) shape, i think anyways. may be wrong

[brightsky]

doesn't make sense, unless you mean 'intersection'.

[Jayward]

i read it as (|z| < 3) intersection (|z|>1)

[ahat]

I have this graph, 1 ≤ x²+ y²  ≤9, i.e. a circle with centre (0, 0) defined between 1 and 3.

I have a range of other options which I have to explain why they are wrong, but I don't really have a clue what {z: (|z| ≤ 3) - (|z| ≤ 3)} is. This is exactly how it's written. Can anyone provide some insight?

[ahat]

***{z: (|z| ≤ 3) - (|z| ≤ 1)}

[ashs_vb]

center at(0,0) for both and we are talking about are hence
[mod(z)<=3] is a circle with the radius 3
[mod(z)<=1] is a circle with the radius 1

As they are representing area subtract the are of the circle with radius 1 from the larger circle and as Jayward said it will be an annulus.

[BubbleWrapMan]

It should be written as . If you actually subtract the inequalities you end up with , which is the entire complex plane.