I've been in trouble enough lately, I figured I would get up to speed on a few things. Pondering elementary Complex Analysis, I made it only to page 53 before I managed to get stuck.

I want a non-zero Harmonic Function that disappears on the hyperbola y = 1/x.

I'm staring at f(z) = z^2.

I created a lovely page (or 3) of algebraic manipulations that lead to interesting results and relationships, but don't solve the problem at hand. I figure I'm just missing something.

Do I get a hint? What about f(z) = z^2 is supposed to impress me?