It is a fact, which we can verify by cubing, that the zeros of x'– 2 in Q are a2 = V2+iv3 where 2, as usual, is the real cube root of 2. Use this information in Exercises 4 through 6. aj = V2. =タニ!ーiv3 COLLEbouq& to pe CAnnopowoobpra oK KGrT and

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.7: Distinguishable Permutations And Combinations
Problem 21E
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Section 49 number 4
It is a fact, which we can verify by cubing, that the zeros of x' - 2 in Q are
meidqiomomo.goitautevo o o gaibmogagTIo
a3 = 21-i3
where 2, as usual, is the real cube root of 2. Use this information in Exercises 4 through 6.
aj = V2.
a2 = 2+iv3
and
4. Describe all extensions of the identity map of Q to an isomorphism mapping Q(2) onto a subfield of Q.
Describe all extensions of the dentity map of O to an isomorphism mapping 2,ente auhfiald
6. Deserbe al"
Onte a subfield of O
f the auwmorphism y /3.-vs /3) to an isomorphism mapping C,
Transcribed Image Text:It is a fact, which we can verify by cubing, that the zeros of x' - 2 in Q are meidqiomomo.goitautevo o o gaibmogagTIo a3 = 21-i3 where 2, as usual, is the real cube root of 2. Use this information in Exercises 4 through 6. aj = V2. a2 = 2+iv3 and 4. Describe all extensions of the identity map of Q to an isomorphism mapping Q(2) onto a subfield of Q. Describe all extensions of the dentity map of O to an isomorphism mapping 2,ente auhfiald 6. Deserbe al" Onte a subfield of O f the auwmorphism y /3.-vs /3) to an isomorphism mapping C,
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