All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)

Graph of 2(i)
Graph of 2(i)

(ii)
(a)
Required answer = \sqrt{7^2 + 3^2} -4 = \sqrt{58} - 4

(b)
z = 7 - 4 cos (tan^{-1}\frac{3}{7}) - i(3 - 4sin (tan^{-1}\frac{3}{7}))

z = 7 - 4 (\frac{7}{\sqrt{58}}) - i(3 - 4(\frac{3}{\sqrt{58}}))

z = 7 - \frac{28}{\sqrt{58}} - i(3 - \frac{12}{\sqrt{58}})

(iii)
arg(z) = - tan^{-1} \frac{3}{7} - sin^{-1} \frac{4}{\sqrt{58}} = -0.9579 \mathrm{~radians}

KS Comments:

For (iib), students should draw the right angled triangle out to see what the value is since its required that they leave in exact form. When there is a circle for locus, I usually remind students to always utilise the radius.

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