10. Singularities

Poles — Quiz

Test your understanding of poles with 5 practice questions.

Practice Questions

Question 1

Which statement best describes a pole at $z_0$?

Question 2

What is the order of the pole of $f(z)=\frac{1}{(z-2)^3}$ at $z=2$?

Question 3

What is the order of the pole of $f(z)=\frac{z-2}{(z-2)^5}$ at $z=2$?

Question 4

The Laurent series of $f$ about $z_0$ is $f(z)=\frac{5}{(z-z_0)^2}-\frac{1}{z-z_0}+7+\cdots$. What is the order of the pole at $z_0$?

Question 5

What type of singularity does $f(z)=\frac{\sin z}{z}$ have at $z=0$?