# Complex - Harmonic, mainly derivative question

1. Sep 16, 2006

### mattmns

I have the following exercise:

Verify that $$\frac{y}{(x-1)^2 + y^2}$$ is harmonic for $(x,y) \neq (1,0)$
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Now I know how to do this, just find the second partials of u with respect to x and with respect to y, and see if their sum is 0. However, after looking at the first partials, it seems as though taking the second partials is going to be ugly. Is there some slick way out of doing a bunch of tedious algebra, or I am just going to have to do it? The question actually has two more parts; namely, (ii) find the harmonic conjugate u, and (iii) write the analytic function w = u+iv as a function of z. So a slick trick would help dramatically Thanks!

Last edited: Sep 16, 2006