Question

Show that u is harmonic and find all of its harmonic conjugates.

\[u(x,y)=\frac{x}{x^{2}+y^{2}}\]

Answer 1

harmonic uxx+uyy=0 that can be done, the conjugates are a little trickier

Answer 2

now that i think about it, this one is too hard to do on message board so i'll keep trying it on paper