Your Practice Set – Applications and Interpretation for IBDP Mathematics
20
Paper 1 – Moduli and Arguments
Example
Consider the complex number
5i z � , where z � .
3 � 4i
( 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 ]
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Solution
( a )
5i z � 3 � 4i
4 3 z � � i A2
5 5
( b ) The modulus of z
�
� 1 � 1
2 2
� 4 3 � � � � � � �
� � 5� � 5�
( c ) The argument of z � 3 � � arctan 5 � � � 4
� � � � 5 �
�3 �
� arctan � � � 4 �
� 0.6435011088 rad
M1
A1
M1
� 0.644 rad A1
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[ 2 ]
[ 2 ]
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