Consider the conjugate mapping T : C → C that is T(z) = z where z E C, or T(a + bi) = a – bi where a, b E R. a. Show that T is not linear if C is viewed as a vector space over itself. b. Show that T is linear if C is viewed as a vector space over the real field R.

Consider the conjugate mapping T : C → C that is T(z) = z where z E C, or T(a + bi) = a – bi where a, b E R. a. Show that T is not linear if C is viewed as a vector space over itself. b. Show that T is linear if C is viewed as a vector space over the real field R.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

6. Consider the conjugate mapping T : C → C that is T(z)
T(a + bi)
= 7 where z E C, or
= a – bi where a, b e R.
a. Show that T is not linear if C is viewed as a vector space over itself.
b. Show that T is linear if C is viewed as a vector space over the real field R.

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