A totally imaginary number field is a specific type of number field where every element of the field has its conjugates (in terms of field embeddings into the complex numbers) lying on the imaginary axis. More precisely, a number field is a finite extension of the field of rational numbers \(\mathbb{Q}\).
Articles by others on the same topic
A number field is totally imaginary if it has no embedding into the real numbers. Its embeddings into the complex numbers occur entirely in conjugate pairs. This is also called totally complex; it does not assert that every element of the field is nonreal.