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1
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PT@ 30
WR@50
MHS Bball gape
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Nina L
Chapter 10 Take Home Assessment
(a) Express $-3 + \sqrt{3}i$ in the form $re^{i\theta}$, where $r > 0$ and $-\pi < \theta \le \pi$.
[5]
Let the roots of the equation $z^3 = -3 + \sqrt{3}i$ be $u$, $v$ and $w$.
(b) Find $u$, $v$ and $w$ expressing your answers in the form $re^{i\theta}$, where $r > 0$ and $-\pi < \theta \le \pi$.
[5]
On an Argand diagram, $u$, $v$ and $w$ are represented by the points U, V and W respectively.
(c) Find the area of triangle UVW.
[4]
(d) By considering the sum of the roots $u$, $v$ and $w$, show that
$\cos \frac{5\pi}{18} + \cos \frac{7\pi}{18} + \cos \frac{17\pi}{18} = 0$.
[4]
