Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
3.21. A quarternion is an ordered pair of complex numbers; e.g., ((1,2), (3, 4)) and (2+i, 1-i). The sum of quarternions (A, B) and (C, D) is defined as (A + C, B + D). Thus, ((1, 2), (3, 4)) + ((5, 6), (7,8)) = ((6,8), (10, 12)) and (1 – i, 4 + i) + (7+ 2i, -5 + i) = (8+i, -1+ 2i). Similarly, the scalar multiplication by a complex number A of a quaternion (B, C) is defined by the quadternion (AB, AC). Show that the addition and scalar multiplica- tion of quaternions satisfy all the properties of addition and multiplication of real numbers.

3.21. A quarternion is an ordered pair of complex numbers; e.g., ((1,2), (3, 4)) and (2+i, 1-i). The sum of quarternions (A, B) and (C, D) is defined as (A + C, B + D). Thus, ((1, 2), (3, 4)) + ((5, 6), (7,8)) = ((6,8), (10, 12)) and (1 – i, 4 + i) + (7+ 2i, -5 + i) = (8+i, -1+ 2i). Similarly, the scalar multiplication by a complex number A of a quaternion (B, C) is defined by the quadternion (AB, AC). Show that the addition and scalar multiplica- tion of quaternions satisfy all the properties of addition and multiplication of real numbers.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
I need the answer as soon as possible
3.21. A quarternion is an ordered pair of complex numbers; e.g., ((1,2), (3, 4)) and (2+i, 1-i). The sum of quarternions (A, B) and (C, D) is defined as (A + C, B + D). Thus, ((1, 2), (3, 4)) + ((5, 6), (7, 8)) = ((6,8), (10, 12)) and (1 – i, 4 + i) + (7+ 2i, -5 + i) = (8+i, -1+ 2i). Similarly, the scalar multiplication by a complex number A of a quaternion (B, C) is defined by the quadternion (AB, AC). Show that the addition and scalar multiplica- tion of quaternions satisfy all the properties of addition and multiplication of real numbers.
Transcribed Image Text:3.21. A quarternion is an ordered pair of complex numbers; e.g., ((1,2), (3, 4)) and (2+i, 1-i). The sum of quarternions (A, B) and (C, D) is defined as (A + C, B + D). Thus, ((1, 2), (3, 4)) + ((5, 6), (7, 8)) = ((6,8), (10, 12)) and (1 – i, 4 + i) + (7+ 2i, -5 + i) = (8+i, -1+ 2i). Similarly, the scalar multiplication by a complex number A of a quaternion (B, C) is defined by the quadternion (AB, AC). Show that the addition and scalar multiplica- tion of quaternions satisfy all the properties of addition and multiplication of real numbers.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS