What is complex number
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This document discusses the history and properties of complex numbers. It begins by outlining the key topics to be covered: history, number systems, complex numbers themselves, and operations. It then provides details on who originally introduced complex numbers and the symbols used. Complex numbers combine real and imaginary numbers and can be expressed as a + bi, where a is the real part and b is the imaginary part. The document also describes how complex numbers extend the number line to the complex plane and defines the basic operations of addition, subtraction, multiplication, and division of complex numbers.
What is complex number
- 2. Presented by: Hamza Sajjad (Complex Number) 2
- 3. History. Number System. Complex numbers. Operations. (Complex Number) 3
- 4. Complex numbers were first introduced by G. Cardano R. Bombelli introduced the symbol 푖. A. Girard called “solutions impossible”. C. F. Gauss called “complex number” (Complex Number) 4
- 5. (Complex Number) 5 Real Number Irrational Number Rational Number Natural Number Whole Number Integer Imaginary Numbers
- 6. When we combine the real and imaginary number then complex number is form. (Complex Number) 6 Real Number Imaginary Number Complex Number
- 7. • A complex number is a number that can b express (Complex Number) 7 in the form of "a+b풊". • Where a and b are real number and 푖 is an imaginary. • In this expression, a is the real part and b is the imaginary part of complex number.
- 8. • 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. (Complex Number) 8
- 9. Complex number extend the concept of one-dimensional number line to the two-dimensional complex plan. (Complex Number) 9
- 10. • Horizontal axis use for real part. • Vertical axis for the imaginary part. (Complex Number) 10
- 11. Complex number convert our visualization into physical things. (Complex Number) 11
- 12. Addition : Complex number added by adding real part in real and imaginary part in imaginary. (a + b푖) + (c + d 푖) = (a + c) + (b + d) 푖. (Complex Number) 12 Subtraction: Similarly, subtraction is defined (a + b푖) - (c + d 푖 ) = (a - c) + (b - d) 푖 .
- 13. (Complex Number) 13 Multiplication: The multiplication of two complex number is define by the following formula: (a + b푖).(c + d 푖 ) =(ac - bd) + (b c + ad) 푖 Square of the imaginary unit is -1. 푖²=푖 ∗ 푖= -1 Division: Division can be defined as: 푎 + 푏푖 푐 + 푑푖 = ( 푎푐+푏푑 푐²+푑² ) ( 푏푐−푎푑 푐²+푑² + )푖