Analysis and Approaches for IBDP Maths Ebook 2 | Page 113

33
Paper 1 Section A – Real and Imaginary Parts
Example
1
(a) Express
4
(1 � i)
in the form
a� bi
, where a , b� .
1
(b) Hence, write down the imaginary part of
4
(1 � i)
.
[5]
[1]
Solution
1 1
(a) �
4
(1 � i) � 4� � 4� � 4�
1 � � �i � � �i � � �i � i
�1� � 2� � 3�
1 1
�
4
(1 � i) 1� 4i � 6( �1) � 4( �i) �1
1 1
��
4
(1 � i) 4
4 2 3 4
(b) 0 A1
M1A1
M1A1
A1
[5]
[1]
9
Exercise 33
1. (a) Express
(b)
3
( 3 � i) in the form a� bi
, where a , b� .
Hence, write down the real part of
3
i( 3 � i) .
z
2. z is a complex number such that 1 0.5i
1� z � � � . Find the imaginary part of z .
3. z is a complex number such that z� z � �4(2 � i) . Find the real part of z .
4. z is a complex number such that z �18 � ( z� 12)i . Find the imaginary part of z .
[5]
[1]
[5]
[5]
[6]
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