Apps. and Interpretation for IBDP Maths Ebook 2 | Page 334

Your Practice Set – Applications and Interpretation for IBDP Mathematics
Exercise 22 z1
22.1 ( a ) ( i ) z
( ii )
2 z z
2�
� 3cis 3
2� i 1 3
2
� 3e
( b )
3
�
2
22.2
( a )
( i )
� zz 1
2�
2 3cis 6
( b ) 3
( ii )
22.3 ( a ) ( i )
( b ) ( i )
( ii ) 2
( ii ) 22.4 ( a ) ( i )
( ii )
( b ) ( i )
Exercise 23
( ii ) z1z2 � 2 3e
�
2
z 1
� 4cis 6
z z
2 1 2
� i 6
5�
� 12cis 12
5� i 2 12 1 2
� 12e z z 1 2� cis 81 3 1
� 162 z2
� � 9cis
4 z 4
1
z z
� i
2 4
� 9e
4 1
23.1 ( a ) The range of f( x ) is { y: y�� 25 }, means the graph of f( x ) does not have
any x -intercept.
( b )
x �2 �
5i
( c )
10
23.2 ( a ) The graph of f( x ) opens upward and the vertex is above the x -axis, means the graph of f( x ) does not have
any x -intercept.
( b )
x � �5 �
8i
( c )
16
23.3
( a )
( i )
8
( ii )
185
( b ) f x a x x
2 ( ) � ( �8 � 185 )
( c )
a �
1
23.4
( a )
( i )
�
1
( ii )
17
4
( b )
� 2 17
� f
( x) � a�x � x �
� � 4
�
( c )
a ��
4
Exercise 24
24.1
( a )
( i )
2
( ii )
3
( b )
� s
3
0.1i 0.25i
( c ) z � w � 2e � � 3e ( d ) ( i ) z �2cis ( � 0.1 )
( ii )
w �
3cis0.25
( e )
( i )
L �
4.93
( ii )
� �
0.110
( f )
S1� S2 � 4.93sin (
6t �
0.110 )
( g ) � 4.93 mm
24.2
( a )
( i )
5
( ii )
7
( b )
2 s
0.9i 1.3i
( c ) z w 5e � � � � � 7e ( d ) ( i ) z �5cis ( � 0.9 )
( ii ) w �7cis ( � 1.3 )
( e )
( i )
L �
11.8
( ii )
� ��
1.13
( f )
W1� W2 �11.8cos (
�t �
1.13 )
( g ) 1.86
324
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