Apps. and Interpretation HL Practice Paper Book | Page 26

Your Practice Paper – Applications and Interpretation HL for IBDP Mathematics

� 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

14

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