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    part a) Sketch on an Argand diagram the circle C whose equation is
    |z - \sqrt 3 - i| = 1

    Part b) Mark the point P on C at which |z| is a minimum. Find this minimum value

    I guessed at \sqrt 3

    part c) Mark the point Q on C at which arg z is a maximum. Find this maximum value.


    Can do part a fine, but I get a different answer for b than the book and don't know how to do c (though I do know it'll be the angle of the tangent from the origin on the top side of the circle.)
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    what does the book say it is? 1?
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    |z| will be smallest closest to 0. How far is sqrt(3) + i from 0? Reduce this by 1 (=radius)

    arg (z) is the angle from 0 to z. So I expect it would be a tangent for maximum value.
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    (Original post by Chaoslord)
    what does the book say it is? 1?
    The book says 3, which I assumed was a mistake.

    I get part B now, do I just have to substitute this point into part c?

    so the answer should be 45 degrees (pi/4) for part c? For this part the book says pi/3, so I think it must have got it totally wrong.
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    I think the point sqrt(3) + i is at distance 2 from the origin.

    So the closest point on the circle is at distance 1.

    If we joint the point 0 to the centre of the circle, it makes an angle pi/6 with the real axis

    Drawing a tangent from the origin makes a 2/1/sqrt(3) triangle

    So I think pi/3 (= pi/6 + pi/6) is right
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    (Original post by ian.slater)
    I think the point sqrt(3) + i is at distance 2 from the origin.

    So the closest point on the circle is at distance 1.

    If we joint the point 0 to the centre of the circle, it makes an angle pi/6 with the real axis

    Drawing a tangent from the origin makes a 2/1/sqrt(3) triangle

    So I think pi/3 (= pi/6 + pi/6) is right
    Ah right Cheers. I got it all now thanks
 
 
 
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Updated: February 9, 2010
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