Please provide Handwritten answer In Exercises 1 through 8, find all conjugates in C of the given number over the given field.1. √2 over Q3. 3 + √2 over Q5. √2+ i over Q7. √1+√2 ovover O

Solution : Conjugate of a real number is, a number which multiply to , The number and it give…

Answered: In Exercises 1 through 8, find all…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.1: Ideals And Quotient Rings

Problem 14E: 14. Let be an ideal in a ring with unity . Prove that if then .

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In Exercises 1 through 8, find all conjugates in C of the given number over the given field. 1. √2 over Q 3. 3 + √2 over Q 5. √√2+i over Q 7. √1 + √2 over Q