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Maths P3-complex number

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I need some help with 7(iii).Its from paper 3 of may/june 2010, variant 1.
 

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u must of drawn a circle of radius 1 and the bisector between (1 and i) from part 2
now draw a line through this shaded region which has the smallest argument. this would obviously be the tangent to the circle. draw this tangent and a line from the radius of the circle to the tangent. now u have a right angled triangle. find the tangent using pythagorus theorem 1 will be the opposite the tangent will be the adjacent and the modulus u found in part (1) which is (root8) is the hypotenus.
so (root8)^2-(1)^2=7
anser is (root7)
 
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