1. Engineering MathematicsⅡ
제13-1 : Complex Number
Complex Plane
제13-2 : Polar form of Complex Number
Powers and Roots

2. Complex Number Why do we use complex number? History of complex number
What is the complex number?

3. Why do we use complex number?

4. History of complex number
“크기가 미묘하여 소용이 없다”

5. History of complex number
X+Yi를 좌표평면
을 이용하여
나타내는 복소평면
기하학적 표현!!

6. Complex Number?

7. Four arithmetical Operations
1. Addition
2. Multiplication

8. Four Arithematical Operations
3. Substraction
4. Division

9. Geometrical representation of complex numbers
Complex Plane
Geometrical representation of complex numbers

10. Geometrical representation of complex numbers

11. Complex Conjugate Numbers

12. Polar Form of Complex Numbers
(1)
(2)
(3)
(“r” is called the absolute value or modulus of z)
(Geometrically |z| is the distance of point z from the origin)

13. is called the argument of z

14. Example 1

15. Polar Form of Complex Numbers
Triangle Inequality

16. We obtain from 6 the generalized triangle inequality
☞ Proof

17. Reversed triangle Inequality

18. Polar Form of Complex Numbers
Multiplication in polar form

19. Polar Form of Complex Numbers
Division in polar form

20. De Moivre’s Formula

21. Roots

22. Roots

23. Taking z=1 |z| = r = 1

24. Roots의 기하학적 표현

25. Roots의 기하학적 표현

26. Example