Q7 7Consider the function T:R² →C defined by T(x,y)=x+iy. Show that this is an isomorphism of realvector spaces. Find at least one other isomorphism between R2 and C. Hint: complex conjugation is an automorphismof C.

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Answered: Consider the function T:R² → C defined…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 27E: 27. Let , where and are nonempty. Prove that has the property that for every subset of if and...

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Consider the function T:R² → C defined by T(x,y)=x+iy. Show that this is an isomorphism of real vector spaces. Find at least one other isomorphism between R2 and C. Hint: complex conjugation is an automorphism of C.