3. Cauchy-Riemann Equations

Examples And Counterexamples — Quiz

Test your understanding of examples and counterexamples with 5 practice questions.

Practice Questions

Question 1

Which complex function has real part $u(x,y)=x^2-y^2$ and imaginary part $v(x,y)=2xy$?

Question 2

Which of the following real-valued functions is harmonic?

Question 3

If $f(z)=u+iv$ is analytic and $u_x=5$ and $u_y=-3$ at a point, what are $v_y$ and $v_x$ at that point?

Question 4

What is $u_{xx}+u_{yy}$ for $u(x,y)=x^2+y^2$?

Question 5

Which function has real part $e^x\cos y$?