Exercise 20
1 . Consider the complex number
2� i z � , where z � . 2 � i
( a ) |
Express z in the form a� ib, where a , b� |
. |
( b ) |
Find the exact value of the modulus of z . |
|
( c ) |
Find the value of the argument of z . |
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2 . Consider the complex number
( a ) Express
2
z in the form
10 24 z � � i , where z � .
13 13
a� ib, where a , b� .
( b ) Find the exact value of the modulus of
( c ) Find the value of the argument of
3 . Consider the complex number
( a ) ( i ) Express
2
z .
2
z .
8 6 z � � i , where z � .
5 5
3
z in the form a� ib, where a , b� .
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6
( ii ) Hence , write down
( b ) Find the exact value of the modulus of
3 * 352 ( z ) � in the form a� ib, where a , b� . 125
3 * 352 ( z ) � .
125
( c ) Write down the exact value of the argument of
3 * 352 ( z ) � .
125
4 . The complex numbers z
1
and z
2 have arguments between 0 and π radians . Given that
2 z1�iz2
� 0, z2 � �2 � 2 ai and z2 � 2 , where a� .
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( a ) Find the modulus of z
1
.
( b ) Find the value of a .
( c ) Hence , find the argument of
2 z
2
.
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