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Maths paper 3 (MAY june 10 paper 31)URGENT!!

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O no 7 (III)
SDC12845.jpg

This is the graph i have drawh for Qno (II)
For (III) MS says draw a tangent to the lowest part of the circle ...i tried it out ...but could not ger the modulus of z....can any help me out with this?
 
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The answer can be easily obtained if you use the Pythagorean Principle. ;)

Here, try to find the right-angled triangle: the origin, the tangent point, and the centre of the circle - these three points form a 90-degree triangle due to the tangent.

Then, the origin to the circle centre (noted as |C.C|) is 2 * sqrt 2 , and the radius of the circle = 1. So (|z|)^2 should be (|C.C|)^2 - radius^2 = 8 - 1 = 7. So |z| = sqrt 7.
 
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