Imaginary Embedding

An imaginary embedding of a number field K is a field embedding sigma:K->C 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 K is the second component of the number field signature.

See also

Complex Conjugate, Complex Number, Field Embedding, Imaginary Number, Number Field Signature, Real Embedding, Totally Imaginary Field

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Cite this as:

Weisstein, Eric W. "Imaginary Embedding." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ImaginaryEmbedding.html

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