Complex Line Integrals I

Part 4: Summary

In this module we have considered a number of properties of line integrals of complex functions. In the summary, we will focus on the line integrals of the two functions f₁(z) = 1/z and f₄(z) = e^z.

1. Summarize the differences you have observed between the line integrals of the two functions.

2. What do you think is the important difference between functions that have line integrals that behave similarly to those of the exponential function and functions that have line integrals that behave similarly to those of the reciprocal function?

3. Study two new functions to see if they support your conjecture in Step 2. If necessary, modify your conjecture and test again.

4. State your final conjecture.