3. Cauchy-Riemann Equations

Derivation And Interpretation — Quiz

Test your understanding of derivation and interpretation with 5 practice questions.

Practice Questions

Question 1

For $f(z)=u(x,y)+iv(x,y)$, which pair of equations is the Cauchy-Riemann system?

Question 2

In the standard derivation of the Cauchy-Riemann equations from the limit definition of $f'(z)$, what is compared?

Question 3

Let $u(x,y)=e^x\cos y$ and $v(x,y)=e^x\sin y$. Do the Cauchy-Riemann equations hold everywhere?

Question 4

If $u_x=5$ and $u_y=-2$ at a point, what must $v_y$ and $v_x$ be for the Cauchy-Riemann equations to hold there?

Question 5

What is the best interpretation of the Cauchy-Riemann equations for a complex differentiable function?