Analysis and Approaches for IBDP Maths Ebook 2 | Page 123

37
Paper 2 Section A – Moduli and Arguments
Example
Consider the complex number
z �
i
3� i
, where z � .
(a) Express z in the form a� ib, where a , b� .
(b) Find the exact value of the modulus of z .
(c) Find the exact value of the argument of z .
[2]
[2]
[2]
Solution
(a)
i
z �
3�
i
i( 3 �i)
z �
( 3 �i)( 3 �i)
z �
3i � i
4
2
3i �� ( 1)
z �
4
M1
9
(b)
1 3
z � � i
A1
4 4
The modulus of z
2
�1�
� 3�
� � � �� �4� � 4 �
� �
2
M1
4
�
16
1
� A1
2
[2]
[2]
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