12 . A geometric series of complex numbers is defined as
4 8 � � � .
5 25
i� 2i�
2 e e
( a ) Find z , where z is the common ratio of the series .
[ 2 ] ( b ) Write down the sum to infinity of this series , giving the answer in terms of i and � . [ 2 ]
( c ) Hence , show that
( i )
( ii )
|
2
4 sin�
� sin
2�
� sin
3�
�
5
25
|
25sin�
�
;
29
�
20cos�
|
|
2
4 cos�
� cos
2�
� cos3�
�
5
25
|
5 ( �2
�5cos �)
�
.
29
�
20cos�
|
[ 15 ]
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