9. Laurent Series

Principal Parts — Quiz

Test your understanding of principal parts with 5 practice questions.

Practice Questions

Question 1

In a Laurent series $f(z)=\sum_{n=-\infty}^{\infty} a_n (z-z_0)^n$, what is the principal part?

Question 2

What is the principal part of $f(z)=e^z$ about $z=0$?

Question 3

For $f(z)=\frac{1}{z(z-1)}$, what is the principal part at $z=0$?

Question 4

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

Question 5

If the Laurent series of $f$ about $z_0$ is $f(z)=2(z-z_0)^{-3}-(z-z_0)^{-1}+4+(z-z_0)$, what is the principal part?