I have $\Im(z)=\ln(x^2+y^2)$ and need to find the harmonic conjugate of it. I'm looking at SO question and its answer Showing that $u(x, \, y) = \ln(x^2 + y^2)$ is harmonic without computing partial derivatives
The answer there is $2\ln z$ but in the book I have it's $2i\ln z$. So what's missing?