9. (i) Find the real numbers x and y such that
x -j— ty 2—b ^ 3 ~b £
(ii) Express \/3 — f in the form r(cos 0 + i sin 9), and find
the three roots of the equation £3 — 4 (-\/3 — i) = 0.
(iii) If a = r (cos a i sin a) and sr = cos 9 + i sin 9, where
r, a, 9 are real and r is positive, show that
\ a\ 2 = (1 + r)2 — 4r sin2^ (0 — a).
Hence show that, if a is such that | £ + a | ^ 2 for all
values of 9, then r < 1.
(C41647)
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