1. Engineering Mathematics
Complex Variables & Applications
Chapter 3
郑伟诗

2. Outline Exponential Function Logarithmic Function Complex Exponents
Wei-Shi Zheng
, Page 2

3. Exponential Function
Definition: 3

4. Exponential Function Equivalent between two complex variables
Wei-Shi Zheng
, Page 4

5. Exponential Function Roots root 16.09.2018, Page 5 Wei-Shi Zheng
, Page 5

6. Exponential Function Sum Rule:
The definition of exponential function is equivalent to the expression:
Sum Rule: 6

7. Exponential Function
>0

8. Exponential Function
*Example 1:
*Solution: 8

9. Exponential Function 9

10. Exponential Function Example 2: Compute the principal angles Solution:
Give the principal value of argument:
Solution: 10

11. Exponential Function 11

12. Exponential Function
Example 3:
Solution: 12

13. Exponential Function
Example 4: ?

14. Logarithmic Function
1.Definition: 14

15. Logarithmic Function

16. Logarithmic Function

17. Logarithmic Function

18. Logarithmic Function
Review

19. Logarithmic Function

20. Logarithmic Function
Branch

21. Logarithmic Function
Branch Cut

22. Logarithmic Function branch cut(including the origin) f(z)
singular points
F(z)
branch

23. Logarithmic Function *Example 4: *Solution: *Remark:
Among Functions of Real Variable, negative numbers do not have logarithm, yet complex variable logarithmic function is the extension of real variable logarithmic function. 23

24. Logarithmic Function
*Example 5:
*Solution: 24

25. Logarithmic Function
*Example 6:
*Solution: 25

26. Logarithmic Function 26

27. Logarithmic Function
Properties: 27

28. Logarithmic Function
Properties: 4) 5) 6) 28

29. Complex Exponents
any complex number
Definition

30. Complex Exponents

31. Complex Exponents
Example