What are the field embeddings from $K\to\bar{\mathbb Q}$ and how can I use these to compute $N_{K/\mathbb Q}(a)$ and $T_{K/\mathbb Q}(a)$, with $K=\mathbb Q({\sqrt[3]{2}})$ and $a={\sqrt[3]{2}}+3$
Now an embedding is a homomorphism between $2$ fields, and here the closure of $\mathbb Q$ is I think $\mathbb R$
Since I had to find the norm and the trace in a different way (with a matrix which is the same as multiplication by a), If I look at the formula below, I guess there should be $3$ such embeddings, because I obtained a $3\times3$ matrix in the previous case.
$N_{K/\mathbb Q}(a)=\prod\limits_{i=1}^{d}\sigma_i(a)$, $\quad$$T_{K/\mathbb Q}(a)=\sum\limits_{i=1}^{d}\sigma_i(a)$
but I have some difficulties to determine them, so any element of $K$, say $r+s{\sqrt[3]{2}}+t{\sqrt[3]{4}}$ is sent to $\mathbb R$, id should be for example one, since its a homomorphism. How can I continue ?