Is there any criterion for a number field whose every embedding to $\mathbb{C}$ is closed under complex conjugate?

Question

I'd love it if there is any easy way to determine whether a given number field (i.e., a finite extension of $\mathbb{Q}$) has the property: the image of every embedding to $\mathbb{C}$ of it is closed under the complex conjugate operation.

Note that the totally real fields, the quadratic fields, $\mathbb{Q}(\sqrt[4]{2})$ and so on are examples, whereas $\mathbb{Q}(\sqrt[3]{2})$ is a non-example.

Any help appreciated.