complex number

1. 1
Complex Number
Name ID No.
Md Rasadul Islam 10116034
Mahay Alam Noyon 10116024
Ahasanul Mahbub Jubayer 10116011
Md Rahat Hossain 10116006
Ashraful Alim 10116029
Group Members

2. 2
Presented By
Md Rasadul Islam

3. 3
• An ordered pair of real number generally
written in the form “a+ib”
• Where a and b are real number and 𝑖 is an
imaginary.
• In this expression, a is the real part and b is
the imaginary part of complex number.
Complex Numbers

4.  When we combine the real and imaginary number
then complex number is form.
4
Real
Number
Imaginary
Number
Complex
Number

5. 5
• A complex number has a real part and an imaginary
part, But either part can be 0 .
• So, all real number and Imaginary number are also
complex number.

6. 6
Complex number extend the concept
of one-dimensional number line to
the two-dimensional complex plan.
• Horizontal axis use for real part.
• Vertical axis for the imaginary part.

7. 7(Complex Number) 7
 Equations like x2=-1 do not have a solution
within the real numbers
12
x
1x
1i
12
i Real no:
Imaginary no:
 Why complex numbers are introduced???

8. 8
:then,1-If i
12
i ii 3
14
i ii 5
16
i ii 7
18
i .etc

9. 9(Complex Number)
i
ii
)53()12(
)51()32(


i83 
Example
Real Axis
Imaginary Axis
1z
2z
2z
sumz
Addition :
Complex number added by adding real part in real
and imaginary part in imaginary.
(a + b𝑖) + (c + d 𝑖) = (a + c) + (b + d) 𝑖.
Fundamental Operations with complex number

10. (Complex Number) 10
Subtraction:
Similarly, subtraction is defined
(a + b𝑖) - (c + d 𝑖 ) = (a - c) + (b - d) 𝑖 .
i
i
ii
21
)53()12(
)51()32(



Real Axis
Imaginary Axis
1z
2z
 2z
diffz
 2z
Example

11. 11(Complex Number)
Multiplication:
The multiplication of two complex number is define by the following
formula:
(a + b𝑖).(c + d 𝑖 ) =(ac - bd) + (b c + ad) 𝑖
Square of the imaginary unit is -1.
𝑖²=𝑖 ∗ 𝑖= -1
i
i
ii
1313
)310()152(
)51)(32(



Example

12. (Complex Number) 12
Division:
Division can be defined as:
𝑎 + 𝑏𝑖
𝑐 + 𝑑𝑖
= (
𝑎𝑐+𝑏𝑑
𝑐²+𝑑²
) + (
𝑏𝑐−𝑎𝑑
𝑐²+𝑑²
)𝑖
EXAMPLE
 
 i
i
21
76

  
 
 
 i
i
i
i
21
21
21
76






22
2
21
147126



iii
41
5146



i
5
520 i

5
5
5
20 i
 i 4

13.  Examples of the application of complex numbers:
1) Electric field and magnetic field.
2) Application in ohms law.
3) In the root locus method, it is especially important whether the
poles and zeros are in the left or right half planes
4) A complex number could be used to represent the position
of an object in a two dimensional plane,
(Complex Number) 13
How complex numbers can be applied to “The Real
World”???

14. (Complex Number) 14

15. 15(Complex Number)
FOR YOUR ATTENTION..!