Analysis and Approaches for IBDP Maths Ebook 2 | Page 122

Your Practice Set – Analysis and Approaches for IBDP Mathematics
(ii)
Hence, find the value of
� 3�
sin � sin .
10 10
(iii)
Find the value of
5
(2r
�1)
�
� cos .
5
r�1
[10]
3. Let w be the solution of the equation
argument.
3
z � � , z � , with the smallest positive
1 0
(a) (i) Express w in its modulus-argument form.
(ii)
Hence, show that
A quartic equation is given by
w w w
2 3
� � � 0 .
4 3 2
z bz cz dz e
� � � � � 0 where b , c , d and e� ,
3 4
z � . The roots of this equation are 1, � 1,
� �w
� w and � , where � � .
[5]
(b) (i) Express � in terms of w .
(ii) Find the value of b .
(iii) Find the value of e .
(iv) Show that c � 0 and d � 1.
[14]
4. (a) Solve the equation
form.
(b)
Hence, solve the equation
5�
5�
Let � �cos
� isin ,
7 7
7
z � � , z � , giving the answers in modulus-argument
1 0
6 5 4 3 2
z z z z z z
� � � � � �1� 0.
4 2
p � � � � � � and
6 5 3
q � � � � � � .
[4]
[4]
(c) (i) Form a quadratic equation of z , z � , with roots p and q .
(ii) Hence, Form a quadratic equation of z , z � , with roots p � 1 and
q � 1.
[12]
112
SE Production Limited