„Komplex konjugált” változatai közötti eltérés

The function <math>\phi(z) = \overline{z}</math> from <math>\mathbb{C}</math> to <math>\mathbb{C}</math> is [[continuous function|continuous]]. Even though it appears to be a "tame" [[well-behaved]] function, it is not [[holomorphic]]; it reverses orientation whereas holomorphic functions locally preserve orientation. It is [[bijective]] and compatible with the arithmetical operations, and hence is a [[field (mathematics)|field]] [[automorphism]]. As it keeps the real numbers fixed, it is an element of the [[Galois group]] of the [[field extension]] <math>\mathbb{C}/\mathbb{R}</math>. This Galois group has only two elements: <math>\phi</math> and the identity on <math>\mathbb{C}</math>. Thus the only two field automorphisms of <math>\mathbb{C}</math> that leave the real numbers fixed are the identity map and complex conjugation.

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[[cs:Komplexně sdružené číslo]]

[[de:Konjugation (Mathematik)]]

[[fr:Conjugué]]

[[it:Complesso coniugato]]