I don't understand this notation.
Calculate $\partial(|z|^2+1)$ and $\bar{\partial}((\bar{z}|z|^2+1)\cdot \sin(z))$
They're asking me to find the derivatives with respect to $z$ and $\bar{z}$ resp.?
In that case, are my solutions correct?
$a)$ $\partial(|z|^2+1)=\partial(\bar{z}z+1)=\bar{z}$
$b)$ $\bar{\partial}((\bar{z}|z|^2+1)\cdot \sin(z))=\bar{\partial}((\bar{z}^2\cdot z+1)\cdot \sin(z))=2\bar{z}z\cdot \sin(z)$
Thanks for your time.