Question 1
Which statement best matches the definition of an analytic function on a domain?
Question 2
If $f=u+iv$ is complex differentiable and $u$ and $v$ have continuous first partial derivatives, which equations must hold?
Question 3
What does the Maximum Modulus Principle say for a nonconstant analytic function on a connected open set?
Question 4
Suppose $f$ is analytic on a connected domain and $f'(z)=0$ for every point in the domain. What follows?
Question 5
If $f=u+iv$ is analytic, which statement is always true about $u$?
