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how that both √2 and i are in Q(i + √2) and conclude [Q(i + √2) : Q] = 4. Find the minimal olynomial of i + √2 over Q.

how that both √2 and i are in Q(i + √2) and conclude [Q(i + √2) : Q] = 4. Find the minimal olynomial of i + √2 over Q.

Advanced Engineering Mathematics
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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Show that both √2 and i are in Q(i + √2) and conclude [Q(i + √2) : Q] = 4. Find the minimal polynomial of i+ √2 over Q.
Transcribed Image Text:Show that both √2 and i are in Q(i + √2) and conclude [Q(i + √2) : Q] = 4. Find the minimal polynomial of i+ √2 over Q.
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