Totally real number field

A totally real number field is a type of number field, which is defined as a finite extension of the field of rational numbers \( \mathbb{Q} \). Specifically, a number field \( K \) is called totally real if every embedding of \( K \) into the complex numbers \( \mathbb{C} \) maps \( K \) into the real numbers \( \mathbb{R} \).