Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
Exercise 1.2.11 Show that conjugation respects multiplication, i.e., Notice that the function C₁ x C₂ = C1 x C₂. (1.47) CIT (1.48) given by conjugation is bijective, i.e., is one-to-one and onto. Indeed, two different complex numbers are never sent to the same number by conjugation. Moreover, every number is the complex conjugate of some number. A function from a field to a field that is bijective and that respects addition and multiplication is known as a field isomorphism. Conjugation is thus a field isomorphism of C to C.
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Transcribed Image Text:Exercise 1.2.11 Show that conjugation respects multiplication, i.e., Notice that the function C₁ x C₂ = C1 x C₂. (1.47) CIT (1.48) given by conjugation is bijective, i.e., is one-to-one and onto. Indeed, two different complex numbers are never sent to the same number by conjugation. Moreover, every number is the complex conjugate of some number. A function from a field to a field that is bijective and that respects addition and multiplication is known as a field isomorphism. Conjugation is thus a field isomorphism of C to C.
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