1 of 30

01

Complex

Numbers

Department of Mathematics & Philosophy

The Open University of Sri Lanka

2 of 30

  • Learning Outcomes
  • Introduction
  • General form of a Complex Number
  • Negative Complex Number
  • Equality of Complex Numbers
  • Operations on Complex Numbers
  • Complex Conjugate
  • Geometrical Representation of Complex Numbers
  • Polar (Trigonometric) form of a Complex Number
  • Multiplication and Division of a Complex Number Polar (Trigonometric) form
  • Graphical Addition and Subtraction

​

​

Content

​

02

3 of 30

Learning Outcomes

 

03

4 of 30

Introduction

  •  

 

04

5 of 30

 

05

Introduction-Cont.,

6 of 30

General form of a Complex Number��

  •  

 

 

 

06

7 of 30

 

07

8 of 30

 

Negative Complex Number

​

08

9 of 30

Equality of Complex Numbers

  •  

09

10 of 30

Operations on Complex Numbers

  • Addition and Subtractions

​

​

  • Multiplication of two Complex Numbers

​

​

  • Division of two Complex Numbers

​

​

10

11 of 30

Addition and Subtraction�

  •  

 

11

12 of 30

Multiplication of two Complex Numbers

  •  

 

12

13 of 30

Division of two Complex Numbers

  •  

13

14 of 30

 

{ Multiplying numerator and denominator by the conjugate of the denominator.}

14

Division of two Complex �Numbers- Cont.,

15 of 30

 

15

Division of two Complex �Numbers- Cont.,

16 of 30

 

 

16

Division of two Complex �Numbers- Cont.,

17 of 30

Complex Conjugate�

  •  

 

 

 

17

18 of 30

 

18

19 of 30

Geometrical Representation of Complex Numbers (Argand Diagram)

  •  

19

20 of 30

Polar (Trigonometric) form of a Complex Number

  •  

20

21 of 30

Polar (Trigonometric) form of a Complex Number-Cont.,

  •  

y

 

O

x

 

 

P

21

22 of 30

 

 

 

 

 

P

O

y

x

22

Polar (Trigonometric) form of a Complex Number-Cont.,

23 of 30

Multiplication and Division of a Complex Number Polar (Trigonometric) Form.

 

23

24 of 30

 

24

Multiplication and Division of a Complex Number Polar (Trigonometric) Form -Cont.,

25 of 30

 

25

26 of 30

Let the points P1and P2 represent the Complex Numbers on an argand diagram.

  •  

26

27 of 30

 

27

28 of 30

Graphical Addition and Subtraction

  •  

y

 

O

x

Im(z)

P1

P2

P

 

 

 

E

28

29 of 30

∴ The sum of the Complex Numbers Z1, and Z2 is represented by the point P such that OP1PP2 is a parallelogram.

Q is the point such that OP1QP2 is a parallelogram. Then the point Q represent the Complex Number Z1-Z2;

Draw the line OQ, parallel and equal to the line P1P2. Then the point Q represent the Complex Number (Z1-Z2).

​

​

P1

y

 

O

x

 

P2

Q

 

 

 

P2’

 

Graphical Addition and Subtraction

​

29

30 of 30

Published by The Open University of Sri Lanka

2015

Course Team

​

Author Web Content Developer

Mr. S.M.Lal Chulawansa Ms.M.S.S.Fernando

Ms.J.I.Y.Jayaweera

30

The Open University of Sri Lanka

Nawala, Nugegoda, Sri Lanka

OER Transformation 2015

​

© 2014, Open University of Sri Lanka (OUSL). OUSL OER is developed by the Centre for Educational Technology and Media. Except where otherwise noted, content on this site is licensed under a Creative Commons Attribution-Non Commercial- Share Alike 3.0 License