show that each of the following collections of numbers forms a group under addition (i) The even integers. (ii) All real numbers of the form a + bsqrt(2) where a,b E Z (iii) All real numbers of the form a + bsqrt(2) where a,b E Q (iV) All complex numbers of the form a + bi where a,b E Z

show that each of the following collections of numbers forms a group under addition (i) The even integers. (ii) All real numbers of the form a + bsqrt(2) where a,b E Z (iii) All real numbers of the form a + bsqrt(2) where a,b E Q (iV) All complex numbers of the form a + bi where a,b E Z

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter1: Equations And Inequalities

Section1.3: Complex Numbers

Problem 107E

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Question

show that each of the following collections of numbers forms a group under addition

(i) The even integers.

(ii) All real numbers of the form a + bsqrt(2) where a,b E Z

(iii) All real numbers of the form a + bsqrt(2) where a,b E Q

(iV) All complex numbers of the form a + bi where a,b E Z

Combination of a real number and an imaginary number. They are numbers of the form a + b , where a and b are real numbers and i is an imaginary unit. Complex numbers are an extended idea of one-dimensional number line to two-dimensional complex plane.

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