Let K/F and f € F[t]. Show the following: If FCR and a = a + ib is a root of f with a, b E R then a = a - ib is also a root of f. Let F then a Q. If m € Z is not a square and a +b√/m € C is a root of f with a, b E Q b√m is also a root of f in C.
Let K/F and f € F[t]. Show the following: If FCR and a = a + ib is a root of f with a, b E R then a = a - ib is also a root of f. Let F then a Q. If m € Z is not a square and a +b√/m € C is a root of f with a, b E Q b√m is also a root of f in C.
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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Field theory, roots
![Let K/F and f € F[t]. Show the following:
If FCR and a = a + ib is a root of f with a, b = R then à = a - ib is also a root
of f.
Let F =
Q. If m € Z is not a square and a +b√m € C is a root of f with a, b E Q
then a - b√m is also a root of ƒ in C.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F36d93af9-1c60-4c54-a265-7600bbfc6b68%2F7926a2fc-7b48-48f5-a478-f7389cdaace3%2F5f3ebtt_processed.png&w=3840&q=75)
Transcribed Image Text:Let K/F and f € F[t]. Show the following:
If FCR and a = a + ib is a root of f with a, b = R then à = a - ib is also a root
of f.
Let F =
Q. If m € Z is not a square and a +b√m € C is a root of f with a, b E Q
then a - b√m is also a root of ƒ in C.
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