Analysis and Approaches for IBDP Maths Ebook 2 | Page 112

Your Practice Set – Analysis and Approaches for IBDP Mathematics
SUMMARY POINTs
�
Forms of complex numbers:
1. z �a � bi
: Cartesian form
2. z � r(cos� �isin �) � rcis�
: Modulus-argument form
3.
z �
i
re �
: Euler form
� Properties of moduli and arguments of complex numbers z
1
and z
2
:
1. z1z2 � z1 z2
2.
z
z
1
�
z
z
1
2 2
3. arg( z1z2 ) �arg z1 � arg z2
1
4. arg � z
�
� � � arg z � arg z
� z2
�
1 2
� If z �a � bi
is a root of the polynomial equation pz ( ) � 0
also a root of pz ( ) � 0
, then
*
z �a � bi is
n
� The roots of the equation z � rcis�
are
1
� � 2k
z r n cis
�
� , k �0,1, 2, , n�
1
n
�
De Moivre’s theorem:
If
n n
z� rcis�
, then z � r cisn�
Solutions of Chapter 9
102
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