Describe the locus

• August 11th 2009, 01:51 AM
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.

• August 11th 2009, 02:04 AM
simplependulum
the modulus is equivalent to the length so it must be positive
• August 11th 2009, 02:07 AM
I'm not sure what you mean by that, does that mean I've done it right?
• August 11th 2009, 04:07 AM
mr fantastic
Quote:

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.
• August 11th 2009, 08:16 PM
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?
• August 11th 2009, 08:33 PM
songoku

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

Quote:

The solution is all values of z inside the circle you found, except for z = -i
• August 12th 2009, 01:00 AM
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.
• August 12th 2009, 02:08 AM
mr fantastic
Quote:

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.
• August 12th 2009, 02:42 AM
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.
• August 12th 2009, 04:31 AM
mr fantastic
Quote:

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.
• August 12th 2009, 05:01 PM
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?
• August 12th 2009, 08:03 PM
mr fantastic
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