11. Residues

Residue Computation — Quiz

Test your understanding of residue computation with 5 practice questions.

Practice Questions

Question 1

If a function has the Laurent expansion $f(z)=\frac{2}{z-z_0}+5+7(z-z_0)+\cdots$ about $z=z_0$, what is its residue at $z=z_0$?

Question 2

What is the residue of $f(z)=\frac{z+1}{z-3}$ at $z=3$?

Question 3

What is the residue of $f(z)=\frac{1}{z^2+1}$ at $z=i$?

Question 4

What is the residue of $f(z)=\frac{\sin z}{z^2}$ at $z=0$?

Question 5

What is the residue of $f(z)=\frac{e^z-1}{z^2}$ at $z=0$?