Analysis and Approaches for IBDP Maths Ebook 2 | Page 287

Answers
Exercise 36
�
36.2 (a) z � cis , 5
3�
z � cis , 5
36.1 (a)
2�
z � cis0 , z � cis , 9
4�
2�
z � cis , z � cis ,
9 3
8�
10�
z � cis , z � cis ,
9 9
4�
14�
z � cis , z � cis 3 9
(b)
(c)
or
(i)
(ii)
16�
z � cis 9
9
z � 1
2�
z � cis , 9
4�
z � cis , 9
8�
z � cis , 9
10�
z � cis , 9
14�
z � cis or 9
16�
z � cis 9
(i) � � � w � w � w
(ii) b �� 1
(iii) d � 0
(iv) c � 0
2 5 8
z � cis�
,
9�
z � cis 5
5
z �
7�
z � cis or 5
(b) (i) 1
(ii)
� 3�
z � cis , z � cis ,
5 5
7�
z � cis or 5
9�
z � cis 5
(c) (i)
� 3�
1
cos �cos
�
5 5 2
(ii)
� 3�
1
sin � sin � �
10 10 2
(iii) 0
36.3 (a) (i)
2�
2�
w �cos
� isin
3 3
(ii) Refer to solution
(b)
(i)
2
� �1�
w
(ii) b �� 1
(iii) e �� 1
(iv) Refer to solution
36.4 (a)
� 3�
z � cis , z � cis ,
7 7
5�
z � cis , z � cis�
,
7
9�
11�
z � cis , z � cis or
7 7
13�
z � cis 7
�
(b) z � cis , 7
3�
z � cis , 7
5�
z � cis , 7
9�
z � cis , 7
11�
z � cis or 7
13�
z � cis 7
(c)
(i)
(ii)
z
z
2
2
� z� 2�
0
� z� 2�
0
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