Analysis and Approaches for IBDP Maths Ebook 2 | Page 120

Your Practice Set – Analysis and Approaches for IBDP Mathematics
(b)
(i)
2 3 4 5
( z �1)(1 � z � z � z � z � z )
� z � z � z � z � z � z
2 3 4 5 6
�1� z � z � z � z � z
2 3 4 5
M1
6
� � A1
z
1
(c)
(ii)
(i)
2 3 4 5
1� z � z � z � z � z � 0
6
z �1 � 0 , where z � 1
M1
z �1
� � 2�
2�
z �cos
� isin , z �cos
� isin ,
3 3 3 3
4�
4�
z �cos� � isin�,
z �cos
� isin
3 3
5�
5�
or z �cos
� isin
A1
3 3
� �
� � �
2 5
( w w w )
�
2 5
� � ( w) � ( w ) � ( w )
�
� � � M1
[4]
6 1 6 2 6 5
� � � � �
� w � w � w
A1
4 5
� � � w� w � w
A1
(ii)
b
� � � � � � M1A1
1
2 5 4 5
w� w � w � w� w � w � � b
2 2 3 3 2 3
w� w � w ( w ) � w� w( w ) � w ( w ) � � b
2 2 2
w� w � w � w� w� w � � b
M1
2
w�
w � � b
2
b �w � w
� � � � � � � �
b � �cos � isin � ��cos � isin �
� 3 3 � � 3 3 �
2� 2� � �
b � cos � isin � cos � isin
3 3 3 3
b �� 1
2
A1
A1
(iii)
c
�� � � M1A1
1
2 5 4 5
( )( )
w� w � w w� w � w � c
w � w � w � w � w � w
2 5 6 3 6 7
� � � �
6 9 10
w w w c
110
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