A totally imaginary field is a field with no real embeddings. A general number field 
of degree 
has 
real embeddings 
and 
imaginary embeddings
(
),
where 
.
If 
,
is totally imaginary; if 
, it is totally real; otherwise it is imaginary but not totally
imaginary.
Totally Imaginary Field
See also
Imaginary Embedding, Imaginary Quadratic Field, Number Field Signature, Real EmbeddingThis entry contributed by David Terr
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Cite this as:
Terr, David. "Totally Imaginary Field." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/TotallyImaginaryField.html