1. MAT 3730 Complex Variables Section 1.3 Vectors and Polar Forms http://myhome.spu.edu/lauw

2. Preview More on Vector Representation of complex numbers Triangle Inequalities Polar form of complex numbers (Need to begin 1.4,may be?)

3. Recall We can identify z as the position vector

4. Recall We can identify z as the position vector

5. Triangle Inequality

6. Geometric Proof of the 1 st Form

8. (Classwork) Algebraic Proof of the 1 st Form

9. Geometric Proof of the 2 st Form

10. 2nd Form from the 1 st Form

11. Polar Form of Complex Numbers

12. Recall We can identify z as the ordered pair (x,y).

13. Polar Form of Complex Numbers We can also use the polar coordinate

14. Polar Form of Complex Numbers We can also use the polar coordinate Note that is undefined if z=0.

15. Polar Form of Complex Numbers We can also use the polar coordinate

16. Example 1

17. Problems 1. 2.

18. The argument of a complex number z is not unique.  is called the Principal Argument if Notation: Property of Arguments

19. Example 1 (Remedy)

20. Example 1

21. Polar Form of Complex Numbers We can also use the polar coordinate

22. Product of Complex Numbers in Polar Form

23. Next Class Read Section 1.4 We will introduce the Complex Exponential and Euler Formula Review Maclaurin Series (Stewart section 12.10?)