2. Further Pure 2

Complex Functions — Quiz

Test your understanding of complex functions with 5 practice questions.

Practice Questions

Question 1

Consider the function $f(z) = z \bar{z}$. Which of the following statements about its analyticity is true?

Question 2

If $f(z)$ is an entire function such that $|f(z)| \le M$ for some constant $M > 0$ for all $z \in \mathbb{C}$, what can be concluded about $f(z)$?

Question 3

Consider the function $f(z) = \frac{\cos(z)}{z}$. What is the residue of $f(z)$ at $z=0$?

Question 4

Evaluate the contour integral $\oint_C \frac{1}{z^2} \, dz$ where $C$ is the unit circle $|z|=1$ traversed counterclockwise.

Question 5

Which of the following functions is a harmonic function?