Answered: prove that Z[x]/(x2+1)≃Z[i], where…

prove that Z[x]/(x2+1)≃Z[i], where Z[i]={a+b√-1|a,b∈Z}. show only injectivity and surjectivity in terms of φ:Z[x]/(x^2+1)→Z[i]. (For example 2+3x+x3(x2+1)→2+3i)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 32E

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prove that Z[x]/(x²+1)≃Z[i], where Z[i]={a+b√-1|a,b∈Z}.
show only injectivity and surjectivity in terms of φ:Z[x]/(x^2+1)→Z[i]. (For example 2+3x+x³(x²+1)→2+3i)

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