1. Polar Form and its Applications
MTH 324
Lecture # 2
Polar Form and its Applications

2. Previous Lecture’s Review
The real number system
The complex number system
Comparison of real system with complex
system

4. Lecture’s outline
Polar Form of complex number
Powers and roots
Comparison with Real analysis

6. Complex number as a vector

7. Modulus
Properties

9. Triangle Inequality
Proof.

13. Set of points in the complex plane
Example

16. Polar Form

17. Cont…
Remark

18. Example:
Solution:

21. Example:
Solution:

25. Principal Argument
Notation
Example

28. De Moivre’s Formula
Applications:
To find power of complex number
To find roots of a non-zero complex number

29. Example:
Solution:

31. Comparison of Real system with Complex
Roots of a complex number are also complex whereas the roots of a real number are not necessarily real.

32. References
A First Course in Complex Analysis with Applications by Dennis G. Zill and Patrick D. Shanahan.