# Complex differentials and measured singular foliations

I'm trying to understand the technical basis of singular foliations for pseudo-Anosov diffeomorphisms, and I've hit a bit of a strange calculation I'm having a hard time verifying/unpacking. In Fathi, Laudenbach and Poénaru, they state without explicitly calculation: $$\mathrm{Im}\sqrt{z^k dz^2} = r^{k/2} \left(r\cos\left(\frac{k+2}2 \theta\right) \, d\theta + \sin\left(\frac{k+2}2\theta\right) \, dr\right)$$ and I'm having a hard time showing this explicitly. I'm mostly confused by what they mean by taking a square root of the symmetric 2-form $$dz^2$$. I thought this would be $$\mathrm{Im}\left(\phi^* z^k dz \right)$$, with $$\phi : \mathbb C \to \mathbb C$$ being a square root branch, but I'm having trouble showing this explicitly. Is anyone familiar with this notation/calculation?