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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: ahat on May 29, 2013, 01:03:54 pm

Title: What kind of graph is (|z| < 3) - (|z| < 1)?
Post by: ahat on May 29, 2013, 01:03:54 pm: help appreciated
Title: Re: What kind of graph is (|z| < 3) - (|z| < 1)?
Post by: Jayward on May 29, 2013, 01:33:34 pm: an annulus (doughnut) shape, i think anyways. may be wrong
Title: Re: What kind of graph is (|z| < 3) - (|z| < 1)?
Post by: brightsky on May 29, 2013, 02:56:56 pm: doesn't make sense, unless you mean 'intersection'.
Title: Re: What kind of graph is (|z| < 3) - (|z| < 1)?
Post by: Jayward on May 29, 2013, 02:58:58 pm: i read it as (|z| < 3) intersection (|z|>1)
Title: Re: What kind of graph is (|z| < 3) - (|z| < 1)?
Post by: ahat on May 29, 2013, 07:16:08 pm: 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?
Title: Re: What kind of graph is (|z| < 3) - (|z| < 1)?
Post by: ahat on May 29, 2013, 07:19:05 pm: ***{z: (|z| ≤ 3) - (|z| ≤ 1)}
Title: Re: What kind of graph is (|z| < 3) - (|z| < 1)?
Post by: ashs_vb on June 02, 2013, 11:50:30 am: 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.
Title: Re: What kind of graph is (|z| < 3) - (|z| < 1)?
Post by: BubbleWrapMan on June 02, 2013, 01:54:24 pm: It should be written as $\left \{ z : |z| \leq 3 \right \} \setminus \left \{ z : |z| \leq 1 \right \}$ . If you actually subtract the inequalities you end up with $\left \{z: 0\leq 2 \right \}$ , which is the entire complex plane.