Norm of a number field

Let $𝐾$ be a number field. Then the Field norm of $𝐾$ is given by

𝑁 𝐾 : ℚ (𝛾) = 𝑛 \prod 𝑖 = 1 𝜎 𝑖 (𝛾)

where $𝜎 𝑖 : 𝐾 ↪ ℂ$ enumerate the field embeddings of $𝐾$ into the complex numbers. alg

Proof

proof