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 Quadratic FieldThis entry contributed by David Terr
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Terr, David. "Totally Imaginary Field." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/TotallyImaginaryField.html