I am working on the following question:
Let $V$ be an $n$ dimensional complex vector space and let $\phi : V \to V$ be a complex linear map. Let $W$ be $V$ considered as a real vector space (of dimension $2n$) and let $\psi$ be the same map $\phi$ considered as a $\mathbb{R}$-linear map $W \to W$. What is the relationship between the complex number $\det \phi$ and the real number $\det \psi$? (Of course, you should prove your claim.)
Does anyone have any advice/hints on how to work with this problem?