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IB Maths AA HL: Complex Numbers - A Complete Summary with Worked Examples £9.66   Add to cart
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IB Maths AA HL: Complex Numbers - A Complete Summary with Worked Examples
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A complete summary containing diagrams and worked examples of the content in Maths AA HL on complex numbers as part of the IB DP curriculum. Page 1 is a cover page. Page 2 details the cartesian form and how to form it. Page 3 + 4 goes over worked examples on the cartesian form as well as the c...

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  • May 28, 2024
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  • 2023/2024
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Complex Numbers

, 4A: Cartesian form
i = F
Worked example :



a .
find
?
b .
Hence ,
solve the equation x -6 + 13 = 0

a .
F = N x F
: 42

b .
x =
-

(b) = 5 -
4(1)(3) s use the quadratic
2 formula
=> 6= # = 4: from part a.


2

=> 6 = 4;
2
=
3 = Li

Conjugate roots


Key Point :




A
complex number
, E ,
can be written in Cartesian form as :

z =
x +
iy
where , y
ER
The real part of the complex number E = 2+
Ly is 2 , denoted
by Re <2) .




The imaginary this is denoted
part Of E isy by Im(z)
:




t .

gifz = 3 -
2i Re(z) =
3 [m(z) = -
2




if then its complex Z, is
= x+
My conjugate ,

zx =
x -


iy

Sums, products and quotients in Cartesian form:


worked example

= = 2+ i and w = 5 -
3;


find :



a .
z + W b .
z -
W C .
zw

a z + w =
2 + i + 5 -3 ; and
group real
imaginary parts
.
>




= 7 -
2i

b .
z -
w = 2 + i -

(5 3i) -




=
2+ i -
5 + 3i

= 3 + 4;

c . zw =
(2 + i) (5 -

3i) ~
expand brackets as usual
2
= 10-Gi + Si-3 ;

= 10 -
Gi + 5i + 3

= 13 -
i

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