6. Cauchy’s Theorem

Simply Connected Domains — Quiz

Test your understanding of simply connected domains with 5 practice questions.

Practice Questions

Question 1

Which statement best describes a simply connected domain in complex analysis?

Question 2

Which set is not simply connected?

Question 3

Which set is simply connected?

Question 4

In the annulus $\{z:1<|z|<2\}$, which closed curve cannot be contracted to a point while staying inside the annulus?

Question 5

If $f$ is analytic on a simply connected domain $D$, what is the value of $\oint_\gamma f(z)\,dz$ for every closed curve $\gamma$ in $D$?