Analysis and Approaches for IBDP Maths Ebook 2 | Page 124

Your Practice Set – Analysis and Approaches for IBDP Mathematics
(c)
The argument of z
�
�
� arctan �
�
�
3 �
�
4 �
1
4
�
�
� arctan( 3)
M1
�
� A1
3
[2]
Exercise 37
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 .
2. Let � � (1 � cos �) � isin�
, where 0
* 2
( � ) , giving the answer in terms of � .
�
��
� . Find the modulus and the argument of
2
[2]
[2]
[2]
[8]
3. Let � �sin� � i cos�
, where 0
answer in terms of � .
�
��
� . Express
2
2
� � in Euler form, giving the
(1 )
[9]
4. The complex numbers z
1
and z
2
have arguments between 0 and π radians. Given that
z1z2 � �2 a � 2i , z1�iz2
� 0 and z2 � 2 , where a� .
(a) Find the value of a .
(b) Find the modulus of z
1 .
(c) Express z
2 in Euler form
[4]
[2]
[3]
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