An imaginary embedding of a number field 
is a field embedding 
whose image
is not contained in R. Imaginary embeddings occur in pairs
of complex conjugates, and applying complex
conjugation after an imaginary embedding gives the other member of the pair.
The number of complex-conjugate pairs of imaginary embeddings of 
is the second component of the number
field signature.
Imaginary Embedding
See also
Complex Conjugate, Complex Number, Field Embedding, Imaginary Number, Number Field Signature, Real Embedding, Totally Imaginary FieldExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Imaginary Embedding." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ImaginaryEmbedding.html