Show that conjugation respects multiplication, i.e.. C₁ C₂ = C1 C₂.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f7775f3-edad-4f27-ba1b-f7886a7505bd%2F3ebeecfb-78db-40cb-b210-08c448a66ed6%2Fkk1fsba_processed.jpeg&w=3840&q=75)
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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