Question

August October CHIPOT ME Thursday Friday Sa 1 2 3 PT@ 30 WR@50 MHS Bball gape Snowboar 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]

          August
October
CHIPOT
ME
Thursday
Friday
Sa
1
2
3
PT@ 30
WR@50
MHS Bball gape
Snowboar
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]

August
October
CHIPOT
ME
Thursday
Friday
Sa
1
2
3
PT@ 30
WR@50
MHS Bball gape
Snowboar
Nina L
Chapter 10 Take Home Assessment
(a) Express -3 + √(3)i in the form re^iθ, where r > 0 and -π < θ≤π.
[5]
Let the roots of the equation z^3 = -3 + √(3)i be u, v and w.
(b) Find u, v and w expressing your answers in the form re^iθ, where r > 0 and -π < θ≤π.
[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(5π)/(18) + cos(7π)/(18) + cos(17π)/(18) = 0.
[4]

Added by Adri-N T.

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