MATH 406: Additional Problems for PS 5

1. Show explicitly whether or not the following functions are analytic by checking the Cauchy-Riemann equations:

a)    b)    c)

2. State why the function is entire.

3. Is the function analytic? Show why or why not.

4. Show explicitly that .

5. Let be analytic in . Show that

are harmonic in , and that is a harmonic conjugate of .

6. For each given function, find a harmonic conjugate: a) ; b) .

Andrew L. Belmonte 2005-02-07