Ta có:

$z=\frac{\left( 1-3i \right)\left( 3+i \right)}{1+i}=\frac{6-8i}{1+i}=\frac{\left( 6-8i \right)\left( 1-i \right)}{\left( 1+i \right)\left( 1-i \right)}=-1-7i$

$\begin{align}  & \Rightarrow w=-1+z+{{z}^{2}}=-1+\left( -1-7i \right)+{{\left( -1-7i \right)}^{2}} \\  & =-50+7i \\  & \Rightarrow \operatorname{Re}\left( w \right)=-50 \\ \end{align}$

Vậy đáp án đúng là B.