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# AQA FP2 Loci on argand diagrams stuff. watch

1. part a) Sketch on an Argand diagram the circle C whose equation is

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

I guessed at

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.)
2. what does the book say it is? 1?
3. |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.
4. (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.
5. 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
6. (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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