5. Contours and Complex Integration

Estimation — Quiz

Test your understanding of estimation with 5 practice questions.

Practice Questions

Question 1

Suppose $C$ is a contour of length $10$ and $|f(z)| \le 3$ on $C$. What upper bound does the $ML$ estimate give for $\left| \int_C f(z)\,dz \right|$?

Question 2

What is the length of the line segment from $0$ to $3+4i$?

Question 3

What is the length of the circle $|z|=4$?

Question 4

Let $C$ be the circle $|z|=2$ traversed once counterclockwise. Using the $ML$ estimate, what upper bound is obtained for $\left| \int_C \frac{1}{z}\,dz \right|$?

Question 5

On the unit circle $|z|=1$, what bound does the triangle inequality give for $|z^2+1|$?