Analysis and Approaches for IBDP Maths Ebook 2 | Page 128

Your Practice Set – Analysis and Approaches for IBDP Mathematics
(b)
(ii)
6
z � �
6
z �
z
6
6
(cos isin ) cos 6 isin 6
� � � � � � � A1
6 5 4 2
cos � � 6i cos � sin� �15cos � sin �
3 3 2 4
�20i cos � sin � �15cos � sin � M1
5 6
�6icos� sin � � sin � � cos6� � isin 6�
6 4 2 2 4
cos � �15cos � sin � �15cos � sin �
6 5 3 3
�sin � � i(6cos � sin� � 20cos � sin �
5
�6cos� sin �) � cos 6� � i sin 6�
i 0
�cos 6 � cos �15cos sin
6 4 2
� � � �
2 4 6
�15cos � sin � �sin
�
5
sin 6 � 6cos sin
� � �
3 3 5
�20cos � sin � �6cos� sin �
and
A2
i
� �
�cos
� isin
A1
2 2
� �
�
� �2k�
� 2k�
z cos 2 � � � �
�
isin 2 �
� � � � � �
M1
� 6 � � 6 �
� � � �
( k � 0,1, 2, 3, 4, 5 )
[6]
(c)
� �
�
� �2(0) �
� 2(0) �
z cos 2 � � � �
�
isin 2 �
� � � � � � �
� 6 � � 6 �
� � � �
� �
z �cos
� isin
12 12
�
�r
� 1,
� � A2
12
� � � 6 � 4 � 2 �
cos 6�
� � cos � 15cos sin
�12 � 12 12 12
M1
2 � 4 � 6 �
�15cos sin �sin
12 12 12
6 � 4 � 2 �
0 �cos �15cos sin
12 12 12
A1
2 � 4 � 6 �
�15cos sin �sin
12 12 12
[4]
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