A point in the complex plane with both coordinates rational is called a rational point. The set of rational points on the unit circle will be denoted by C(Q): C(Q) = {a + bi ∈ C | a, b ∈ Q, and a^2 + b^2 =1}. A triple (a,b,c), where a, b, and c are integers, c != 0, and a^2 + b^2 = c^2 is called a Pythagorean triple. Given a Pythagorean triple, can you construct an element of C(Q)? Under this correspondence, when do two different Pythagorean triples give the same element of C(Q)?

A point in the complex plane with both coordinates rational is called a rational point. The set of rational points on the unit circle will be denoted by C(Q): C(Q) = {a + bi ∈ C | a, b ∈ Q, and a^2 + b^2 =1}. A triple (a,b,c), where a, b, and c are integers, c != 0, and a^2 + b^2 = c^2 is called a Pythagorean triple. Given a Pythagorean triple, can you construct an element of C(Q)? Under this correspondence, when do two different Pythagorean triples give the same element of C(Q)?

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter7: Real And Complex Numbers

Section7.2: Complex Numbers And Quaternions

Problem 45E

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