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Modulus on an Argand diagram watch

1. A complex number z satisfies the inequality .

Find the least possible value of

I've drawn a diagram but as far as I can see the lowest value of modulus z is to the point (-1,2) but something is confusing me - is the modulus of z always from the origin?

Anyway I keep getting this wrong and the OCR book is about as useful as a grain of salt. Sorry about the flood of modulus/argument questions - I've missed the past 3 Maths lessons as a result of school trips.
2. Yes the modulus of a complex number is defined to be the distance from the origin.
3. (Original post by around)
Yes the modulus of a complex number is defined to be the distance from the origin.
Right so why do I keep getting it wrong? The answer is 2 which cannot understand..
4. Anyone?
5. Do you know what shape that inequality describes, for a start?
6. (Original post by around)
Do you know what shape that inequality describes, for a start?
Yes, a circle.
7. (Original post by Femto)
Yes, a circle.
Which is the midpoint and radius of this circle?
The proper z (from the origin) points to the point being on the circle or within it.
Which is the nearest point of this circle to the origin?

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Updated: March 22, 2011
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