# Complex analysis- harmonic functions

• Feb 23rd 2009, 01:06 PM
SeanAyres8504
Complex analysis- harmonic functions
I have no idea what the book is talking about with harmonic functions.

1. Find the most general harmonic polynomial of the form ax^2+bxy+cy^2.
(my idea is it is ax? no idea really)

2. Show that if v is harmonic conjugate of u in a domain D, then uv is harmonic in D.

(lost me)
• Feb 23rd 2009, 01:15 PM
HallsofIvy
Quote:

Originally Posted by SeanAyres8504
I have no idea what the book is talking about with harmonic functions.

1. Find the most general harmonic polynomial of the form ax^2+bxy+cy^2.
(my idea is it is ax? no idea really)

There is no "ax", that is a times x^2! Have you considered applying the definition of "harmonic" to ax^2+ bxy+ cy^2? What is $\nabla^2 (ax^2+ bxy+ cy^2)$? What is the definition of "harmonic"?

Quote:

2. Show that if v is harmonic conjugate of u in a domain D, then uv is harmonic in D.

(lost me)
Again, what is the definition of "harmonic conjugate"? If you don't know, you had better look up those definitions. Certainly your teacher expects to know those definitions!