Analysis and Approaches for IBDP Maths Ebook 2 | Page 121

2 5 3 6
w � w �1� w �1 � w( w )
3 6 4 6
�1 � ( ) � ( ) �
w w w w c
2 5 3 4
w w 1 w 1 w 1 1 w c
� � � � � � � � � M1
2 3 4 5
1 1
� w� w � w � w � w � � c
0�1�
c
c � 1
A1
[12]
Exercise 36
1. (a) Solve the equation
form.
(b) (i) Expand
9
z � 1, z �
3 6 3
( z 1)( z z 1)
� � � .
, giving the answers in modulus-argument
[4]
Let
(ii)
Hence, solve the equation
z
� z �1� 0.
6 3
2�
2�
w �cos
� isin . A cubic equation is given by
9 9
3 2
z bz cz d
4 7
d � , z � . The roots of this equation are 1, � � w� w � w and � � .
(c) (i) Express � � in terms of w .
[4]
� � � � 0 where b , c ,
9
(ii) Find the value of b .
(iii) Find the value of d .
(iv) Hence, find the value of c .
[13]
2. (a) Solve the equation
form.
(b) (i) Expand
5
z �1� 0, z � , giving the answers in modulus-argument
4 3 2
( z 1)( z z z z 1)
� � � � � .
[4]
(ii) Hence, solve the equation
� 3�
(c) (i) Find the value of cos � cos .
5 5
4 3 2
z z z z
� � � �1� 0.
[4]
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