Upload
hamza-sajjad
View
90
Download
1
Embed Size (px)
DESCRIPTION
Its a brief note on complex numbers.
Citation preview
1(Complex Number)
(Complex Number) 2
Presented by:Hamza Sajjad
History.
Number System.
Complex numbers.
Operations.
3(Complex Number)
Complex numbers were first introduced by G. Cardano
R. Bombelli introduced the symbol 𝑖.
A. Girard called “solutions impossible”.
C. F. Gauss called “complex number”
4(Complex Number)
5(Complex Number)
Real Number
Irrational Number
Rational Number
Natural Number
Whole Number
Integer
Imaginary Numbers
When we combine the real and imaginary number then complex number is form.
6(Complex Number)
Real Number
Imaginary Number
Complex Number
7(Complex Number)
• A complex number is a number that can b express in the form of "a+b𝒊".
• 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.
8(Complex Number)
• 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.
9(Complex Number)
Complex number extend the concept of one-dimensional number line to the two-dimensional complex plan.
10(Complex Number)
• Horizontal axis use for real part. • Vertical axis for the imaginary part.
11(Complex Number)
Complex number convert our visualization into physical things.
12(Complex Number)
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.
Subtraction:Similarly, subtraction is defined
(a + b𝑖) - (c + d 𝑖 ) = (a - c) + (b - d) 𝑖 .
13(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) 𝑖Square of the imaginary unit is -1.
𝑖²=𝑖 ∗ 𝑖= -1
Division:Division can be defined as:
𝑎 + 𝑏𝑖
𝑐 + 𝑑𝑖= (
𝑎𝑐+𝑏𝑑
𝑐²+𝑑²) (
𝑏𝑐−𝑎𝑑
𝑐²+𝑑²)𝑖+
14(Complex Number)