Let C denote the set of all complex numbers of the form a + bi, where i is defined such that i^2:= −1. Define addition on C by (a + bi) + (c + di) := (a + c) + (b + d)i, and define scalar multiplication by α(a + bi) := αa + αbi, for all real numbers α. Show that C is a vector space over the reals under these operations.

Let C denote the set of all complex numbers of the form a + bi, where i is defined such that i^2:= −1. Define addition on C by (a + bi) + (c + di) := (a + c) + (b + d)i, and define scalar multiplication by α(a + bi) := αa + αbi, for all real numbers α. Show that C is a vector space over the reals under these operations.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.2: Vector Spaces

Problem 37E: Let V be the set of all positive real numbers. Determine whether V is a vector space with the...

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