11 . ( a ) Find the roots of
20 z � which satisfy the condition arg ( ) 0 1
� � � z � ,
2
� expressing your answers in the form rcis� , where r , � � .
Let S be the sum of the roots found in ( a ).
[ 6 ]
( b ) Write down Re S . [ 1 ]
( c ) Show that Re S
1 Im S �� . [ 5 ]
It is given that
� 10 � 2 5 cos � . 10 4
|
( d ) Find the following values , giving the answers in the form
where a , b and c are positive integers :
|
a
� c
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b |
, |
|
� � � ( i ) cos��
� � 5 � ;
|
|
|
|
� 2� �
( ii ) cos��
� � 5 �
3�
10 � 2 5 ( e ) Using ( d ) and cos � 10 4
, show that
[ 6 ]
4 � 2 5 � 10 � 2 5 � 10 � 2 5 Im S �� .
4 [ 2 ]
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