Numerical Analysis. Complex numbers. Chung-Ang University, Jaesung Lee

Transcription

1 Numerical Analysis Complex numbers Chung-Ang University, Jaesung Lee

2 What is a Complex Number? Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 2

3 What is a Complex Number? Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 3

4 What is a Complex Number? Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 4

5 What is a Complex Number? Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 5

6 What is a Complex Number? Real part Imaginary part Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 6

7 What is a Complex Number? Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 7

8 What is a Complex Number? Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 8

9 What is a Complex Number? Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 9

10 What is a Complex Number? Complex conjugate a b Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 10

11 The Algebra of Complex Numbers Addition and subtraction of complex numbers Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 11

12 The Algebra of Complex Numbers Multiplying one complex number by another Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 12

13 The Algebra of Complex Numbers Multiplying one complex number by another Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 13

14 The Algebra of Complex Numbers Dividing one complex number by another Cartesian form Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 14

15 The Algebra of Complex Numbers Dividing one complex number by another Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 15

16 Solutions of Polynomial Equations Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 16

17 Solutions of Polynomial Equations Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 17

18 Argand Diagrams and the Polar Form The Argand Diagram Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 18

19 Argand Diagrams and the Polar Form The Argand Diagram Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 19

20 Argand Diagrams and the Polar Form The Polar Form of a Complex Number Polar coordinates Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 20

21 Argand Diagrams and the Polar Form The Polar Form of a Complex Number Multiplication and division using polar coordinates Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 21

22 Argand Diagrams and the Polar Form The Polar Form of a Complex Number Multiplication and division using polar coordinates Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 22

23 Argand Diagrams and the Polar Form The Polar Form of a Complex Number Complex numbers and rotations Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 23

24 The Exponential Form of a Complex Number Series Expansions for Exponential and Trigonometric Functions a b Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 24

25 The Exponential Form of a Complex Number The Exponential Form a b c Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 25

26 The Exponential Form of a Complex Number Hyperbolic and Trigonometric Functions a b c Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 26

27 De Moivre s Theorem Introduction Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 27

28 De Moivre s Theorem Introduction Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 28

29 De Moivre s Theorem De Moivre s Theorem and Root Finding Arg( ) revisited Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 29

30 De Moivre s Theorem De Moivre s Theorem and Root Finding Arg( ) revisited Numerical Analysis / Chung-Ang University / Professor Jaesung Lee 30