1. 1 Complex powers and trigonometric functions Lecture # 15 MTH 324

2. 2 Complex exponential function Complex logarithmic function Previous Lecture’s Review

3. 3 Complex Powers Complex trigonometric function Lecture’s Outline

4. 4 Complex powers:

5. 5 Remark:

6. 6 Example: Solution:

7. 7

8. 8 Principal value of complex power Example:

9. 9 Solution:

10. 10 Remark:

11. 11 Example: Solution:

12. 12 Example: Solution:

13. 13 Example: Solution:

14. 14

15. 15 Complex trigonometric functions:

16. 16

17. 17 Example: Solution:

18. 18 Example: Solution:

19. 19 Trigonometric Identities

20. 20

21. 21

22. 22 Example: Solution:

23. 23

24. 24 Derivatives:

25. 25

26. 26 Example: Solution:

27. 27

28. 28 References A First Course in Complex Analysis with Applications by Dennis G. Zill and Patrick D. Shanahan. Complex variables and applications by James Brown and Ruel Churchill Fundamentals of complex Analysis by Muhammad Iqbal