1) Define the concept of analytic functions on an open set.

2) Give 3 examples of complex-valued functions that are

differentiable on a point but nowhere analytic.

3) Derive the Cauchy-Riemann equations.

4) Give 3 examples of functions that satisfy the Cauchy-Riemann

equations but not analytic.

5) What are the sufficient conditions for a complex-valued function

to be differentiable at a point?