For a quaternion { = fo + ū let § = 6o_- ū be called the conjugate of {. For any quaternion , show that is a real number and that EE 2 0. Show that if § is nonzero then > 0. Now show that any nonzero quaternion { has a multiplicative inverse o such that go =1 and of = 1. [Hint: show that the inverse is o =

For a quaternion { = fo + ū let § = 6o_- ū be called the conjugate of {. For any quaternion , show that is a real number and that EE 2 0. Show that if § is nonzero then > 0. Now show that any nonzero quaternion { has a multiplicative inverse o such that go =1 and of = 1. [Hint: show that the inverse is o =

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 48E

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