I have this as the imaginary part of $ f(z)$ in Cartesian coordinates, and I need to convert it to polar coordinates.
$$\frac{y^3-b^2y +x^2y }{x^2+y^2} \ \ $$ for $$b>0$$
But I get a really weird expression when changing to polar coordinates that I don’t know how to simplify.
$$\frac{y(x^2+y^2-b^2)}{x^2+y^2}=\frac{r \sin \theta( r^2-b^2)}{r^2}=\frac{\sin \theta(r-b)(r+b)}{r}$$
This is simplified, I don't know if you mean something else..