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    A complex number z satisfies the inequality |z + 2 - 2\sqrt3 i| <= 2.

    Find the least possible value of |z|

    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.
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    Yes the modulus of a complex number is defined to be the distance from the origin.
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    (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..
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    Anyone?
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    Do you know what shape that inequality describes, for a start?
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    (Original post by around)
    Do you know what shape that inequality describes, for a start?
    Yes, a circle.
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    (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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