12. Applications of Residues

Argument Principle Overview, If Included — Quiz

Test your understanding of argument principle overview, if included with 5 practice questions.

Practice Questions

Question 1

Which formula is the argument principle for a meromorphic function $f$ on and inside a simple closed contour $C$ that avoids zeros and poles of $f$?

Question 2

What condition must hold on the contour $C$ before applying the argument principle to $f$?

Question 3

A meromorphic function has $4$ zeros and $1$ pole inside a simple closed contour $C$, counted with multiplicity. What is the value of $\frac{1}{2\pi i}\int_C \frac{f'(z)}{f(z)}\,dz$?

Question 4

What is the contribution of a zero of order $m$ to the count $N$ in the argument principle?

Question 5

What is the contribution of a pole of order $m$ to the count $P$ in the argument principle?