Abstract Algebra: Theory and Applications · Problem 9.4.34

Normal Subgroups and Factor Groups — Thomas Judson

Mathematics — Abstract Algebra · automorphisms

Problem

An automorphism of a group

G

is an isomorphism with itself. Prove that complex conjugation is an automorphism of the additive group of complex numbers; that is, show that the map

\phi(a + bi) = a - bi

is an isomorphism from

\mathbb{C}

\mathbb{C}