24
Paper 2 – Applications of Complex Numbers
Example
Two alternating current electrical sources are given as V1 �4cos ( 4t� 0.1 ) and
V2 � 3cos 4t respectively , where t represents time in seconds . The total voltage V is given by V �V1� V2.
( a ) Write down the amplitude of
( i ) V
1
;
( ii ) V
2
.
( b ) Find the period of V
2
.
4i t
It is given that V1� V2 � Re ( e ( z � w))
, z , w� .
( c ) Find the expression of z� w.
( d ) Express the following in the form r( cos�
� isin �) :
[ 2 ]
[ 2 ]
[ 3 ]
6
( i ) z
( ii ) w
( e ) It is given that i z �w � Le � . Find
[ 2 ]
( i ) L ;
( ii ) � .
4i t
( f ) Using V1� V2 � Re ( e ( z � w))
, express V in the form Acos ( Bt � C) , A , B ,
C � .
( g ) Hence , find the total voltage when t � 1.
[ 6 ]
[ 3 ]
[ 2 ] www . seprodstore . com
69