# Math Help - Describe the locus

1. ## Describe the locus

I'm not sure about this problem (see attachment) as I haven't come across one with a lower constaint. I think it just means the locus can't be below 0. If that's the case then I think I've done it correctly, but I have posted my working (see attachment) just to be sure.

2. the modulus is equivalent to the length so it must be positive

3. I'm not sure what you mean by that, does that mean I've done it right?

I'm not sure what you mean by that, does that mean I've done it right?
The solution is all values of z inside the circle you found, except for z = -i.

5. mr fantastic,

The question only asks to describe the locus, not find any solutions of z. I'm assuming the circle I have found is correct?

Yes, your circle is correct. And when you describe the locus, you should pay attention to what mr fantastic has said

The solution is all values of z inside the circle you found, except for z = -i

7. songoku and mr fantastic,

I haven't usually gone into that much detail when describing the locus. What I essentially put is all I needed for my exercises.

mr fantastic,

The question only asks to describe the locus, not find any solutions of z. I'm assuming the circle I have found is correct?
$|z + i| = 2$ defines a locus (the circle you found).

However .... $0 < | z + i| < 2$ does not define a locus, it defines a region. The region is a punctured disk, described in my earlier post.

9. mr fantastic,

That is why I say the interior of the circle, centred at (0,-1) with radius 2. Not just the circle centred at (0,-1) with radius 2.

mr fantastic,

That is why I say the interior of the circle, centred at (0,-1) with radius 2. Not just the circle centred at (0,-1) with radius 2.
But it's not the entire interior ..... z = -i (the centre) is excluded.

11. mr fantastic,

I’m not sure how you found that the locus can not be equal to z=-i, if it has to do with the fact that 0<, and then it can’t equal –i, this was my original question, as I wasn’t sure about this. This just means then, the locus is the interior of the circle, centred at (0,-1) with radius 2 excluding z=-i. Is this correct?

mr fantastic,

I’m not sure how you found that the locus can not be equal to z=-i, if it has to do with the fact that 0<, and then it can’t equal –i, Mr F says: Correct.

this was my original question, as I wasn’t sure about this. This just means then, the locus is the interior of the circle, centred at (0,-1) with radius 2 excluding z=-i. Is this correct? Mr F says: Yes.
..

13. Okay, mr fantastic, got it, thanks for the help.