/sci/ - Science & Math

I feel really stupid for asking these. I have the following formula for trace

[math] \text{Tr}_K^E(\alpha)=\tfrac{n}{t} \sum_{i=1}^t \phi_i(\alpha) [\math]

where [math] \phi_1,...,\phi_t [\math] are the distinct K-homomorphisms from E into the closure of K.

I feel like both of these should immediately follow from t<n or t=n respectively. The only thing I got from Google/stackexchange was a quick proof using Dedekind's lemma, but we never covered that in our class. Can some kind anon at least provide me with a hint?