The document is a presentation on the Argand diagram, which is a graphical representation of complex numbers in the Cartesian coordinate system. It covers concepts such as the polar form of complex numbers, modulus, and argument, as well as the uses of the Argand diagram for graphical operations like addition and multiplication. Examples of complex numbers and their representations are also provided.

1. Argand Diagram
Presented by:
Mariam Akter
ID: 17511017
Welcome to the presentation
on

2. -3 -2 -1 0 1 2 3
-3 -2 -1 0 1 2 3
Number line
Cartesian coordinate
system (x-y plane)
One dimensional:
• 3
• -2
Two dimensional:
• (3,2)
• 5 + 4 i =(5,4)
Y
X

3. (Real axis)
(Imaginary axis)
Y
X
5
4
(5,4)
Jean-Robert Argand
Argand Plane

4. Let,
Z= x+iy
Where,
x=R(x+iy)
y=I (x+iy)
(Real axis)
(Imaginary axis)
A(x,y)
Z=x+iy
Y
X
What is Argand Diagram?
• Graphical
representation of Z

5. 1. A= 3+4i
2. B= 3-4i
3. C= -7-3i
4. D= 2i
5. E= 9
= 9+0i
-1
-2
-3
-4
-5
-6
-7
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
7
6
5
4
3
2
1
A
B
C
D
E
Graphical Representation Example

6. Polar Form
Modulus: r = IzI = 𝑥2 + 𝑦2
Argument: 𝜃 = arg z = tan−1 𝑦
𝑥
− 𝜋 < arg 𝑧 ≤ 𝜋
Z=x+iy
𝜃 = arg z
r = IzI
The mod-arg form of z is
z= r (cos𝜃 + isin𝜃)
= r ⅇⅈ𝜃
= r cis 𝜃
Where,
x =r cos𝜃
y= r sin𝜃

7. Example:
z= 4cis120°
= 4(cos120°+ isin120°)
So, r=4 and
𝜃 = 120°
120°
4
z
The real axis
The imaginary axis

8. What is the use of Argand
Diagram?
• Graphical Representation
• Graphical Addition
• Graphical Subtraction
• Graphical Multiplication

9. Thank You 

10. Any question?