Totally imaginary number field
In algebraic number theory, a number field is called totally imaginary (or totally complex) if it cannot be embedded in the real numbers. Specific examples include imaginary quadratic fields, cyclotomic fields, and, more generally, CM fields.

Any number field that is Galois over the rationals must be either totally real or totally imaginary.

References
Section 13.1 of 

Algebraic number theory