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Complex Numbers
� Terminologies of complex numbers : i�
� 1: Imaginary unit z �a � bi : Complex number in Cartesian form a : Real part of z b : Imaginary part of z
* z �a � bi : Conjugate of z �a � bi
2 2 z � r � a � b : Modulus of z �a � bi
arg ( z) ��
� arctan b : Argument of z �a � bi a
� Properties of Argand diagram : 1 . Real axis : Horizontal axis 2 . Imaginary axis : Vertical axis
� 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 www . seprodstore . com
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