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1. In the following item a field K and a complex number a is given. Find the minimal polynomial of a and the degree of a over K. O a. K = Q.a = √3+1. b. K=Q, a = √2 + √/2. c. K = Q, a = 1 but a / 1. d. K = Q(√-1), a = √2. e. K = Q(√2), a = √2. f. K = Q, a = 1 but a # 1, p is prime.

1. In the following item a field K and a complex number a is given. Find the minimal polynomial of a and the degree of a over K. O a. K = Q.a = √3+1. b. K=Q, a = √2 + √/2. c. K = Q, a = 1 but a / 1. d. K = Q(√-1), a = √2. e. K = Q(√2), a = √2. f. K = Q, a = 1 but a # 1, p is prime.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.5: Systems Of Linear Equations In More Than Two Variables
Problem 43E
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1. In the following item a field K and a complex number a is given. Find the minimal polynomial of a and the degree of a over K. O a. K = Q.a = √3+1. b. K=Q, a = √2 + √/2. c. K = Q, a = 1 but a / 1. d. K = Q(√-1), a = √2. e. K = Q(√2), a = √2. f. K = Q, a = 1 but a # 1, p is prime.
Transcribed Image Text:1. In the following item a field K and a complex number a is given. Find the minimal polynomial of a and the degree of a over K. O a. K = Q.a = √3+1. b. K=Q, a = √2 + √/2. c. K = Q, a = 1 but a / 1. d. K = Q(√-1), a = √2. e. K = Q(√2), a = √2. f. K = Q, a = 1 but a # 1, p is prime.
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