Complex multiplication/Real determinant/Exercise

Let ${}z\in \mathbb {C}$ and let

$\mathbb {C} \longrightarrow \mathbb {C} ,w\longmapsto zw,$

be the associated multiplication. Compute the determinant of this map, considering it as a real-linear map

${}\mathbb {R} ^{2}\rightarrow \mathbb {R} ^{2}$.

Create a solution