Consic and b whose divisic demor exist r

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.4: Complex And Rational Zeros Of Polynomials
Problem 36E
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16 Consider the set of complex numbers of the form a + bơ, where a
and b are integers and o = V-2. Draw a grid of parallelograms
whose grid-points consist of these numbers. Demonstrate that
division with remainder is possible in this context; in other words,
demonstrate that if x,y are such numbers, with y # 0, then there
exist numbers q,r such that x =
qy + r, and |r| < \y\.
Transcribed Image Text:16 Consider the set of complex numbers of the form a + bơ, where a and b are integers and o = V-2. Draw a grid of parallelograms whose grid-points consist of these numbers. Demonstrate that division with remainder is possible in this context; in other words, demonstrate that if x,y are such numbers, with y # 0, then there exist numbers q,r such that x = qy + r, and |r| < \y\.
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