- 1 (102.28 KiB) Viewed 36 times
11. [Maximum mark: 18] (a) Express -3+√3i in the form rei, where r>0 and < 0≤π. Let the roots of the equation z³ = −3+√√
-
answerhappygod
- Site Admin
- Posts: 899604
- Joined: Mon Aug 02, 2021 8:13 am
11. [Maximum mark: 18] (a) Express -3+√3i in the form rei, where r>0 and < 0≤π. Let the roots of the equation z³ = −3+√√
11. [Maximum mark: 18] (a) Express -3+√3i in the form rei, where r>0 and < 0≤π. Let the roots of the equation z³ = −3+√√3i be u, v and w. (b) Find u, v and w expressing your answers in the form rei, where r>0 and -<0≤π. 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. (d) By considering the sum of the roots u, v and w, show that 7π 17π = 0. 18 18 COS 5π 18 (b) (c) + cos 12. [Maximum mark: 21] + Cos The function f is defined by f(x) = sinx (a) Find the first two derivatives of f(x) and hence find the Maclaurin series for f(x) up to and including the x² term. Show that the coefficient of x³ in the Maclaurin series for f(x) is zero. Using the Maclaurin series for arctanx and e³x - 1, find the Maclaurin series for arctan (e³x - 1) up to and including the x³ term. f(x) - 1 x=0 arctan(e* − 1) (d) Hence, or otherwise, find lim [5] [5] [4] [4] [8] [4] [6] [3]
Join a community of subject matter experts. Register for FREE to view solutions, replies, and use search function. Request answer by replying!