1. MAT 3730 Complex Variables Section 1.1 The Algebra of Complex Numbers http://myhome.spu.edu/lauw

2. Preview Definitions, Notations Some materials from section 1.2

3. Complex Number System In order to solve the equation we need to expand the real number system (R) to include

4. Definition A Complex Number is an expression of the form Two numbers are the same iff

5. Notations C = collection of all complex numbers

6. Definition

7. Complex Conjugate of z Modulus/ Absolute Value of z

8. Operations

9. Example 1

10. Operations

11. Example 2

12. Things we take for granted…

13. Properties

14. Geometry of Complex Numbers We can identify z as the ordered pair (a,b). Thus, we can represent z as the point (a,b) in the xy-plane.

15. Geometry of Complex Numbers We can identify z as the ordered pair (a,b). Thus, we can represent z as the point (a,b) in the xy-plane (Sect. 1.2)

16. Geometry of Complex Numbers We can also identify z as the position vector (Sect. 1.3)

17. Geometry of Complex Numbers We can also identify z as the position vector (Sect. 1.3)

18. Geometry of Complex Numbers In these contexts, the xy-plane is referred as the Complex Plane

19. Example 3

20. Example 4

21. Next Class Read section 1.2