Quaternion Multiplication: Expanding and Simplifying

Click For Summary

Homework Help Overview

The problem involves expanding and simplifying the product of two quaternions, specifically (3 + 2i + 3j + 4k)(3 + 3i + 2j + 5k). The original poster seeks justification for the method of expanding brackets in quaternion multiplication.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the validity of expanding brackets in quaternion multiplication and question the necessity of this approach. Some suggest that it is based on the definitions of quaternion multiplication and addition.

Discussion Status

The discussion has provided helpful insights regarding the justification for expanding brackets in quaternion multiplication. Participants have explored the underlying definitions and properties of quaternions, contributing to a productive dialogue without reaching a definitive conclusion.

Contextual Notes

There may be assumptions regarding the properties of quaternion multiplication, particularly its distributive nature over addition, which are being examined in the discussion.

flash
Messages
66
Reaction score
0

Homework Statement


Expand and simplify the product of two quaternions:

(3 + 2i + 3j + 4k)(3 + 3i + 2j + 5k)

Justify your response.


The Attempt at a Solution



I have done this by expanding brackets normally, keeping the ijk's in the same order because the multiplication is not commutative. I have the correct answer, I just can't think how to justify it. Why should expanding brackets necessarily work?
 
Physics news on Phys.org
flash said:
Why should expanding brackets necessarily work?

Isn't that how multiplication of the quaternions is defined?
 
Last edited:
flash said:
Why should expanding brackets necessarily work?

It works necessarily because quaternion multiplication distributes over quaternion addition per the definitions of quaternion multiplication and addition.
 
Thanks guys, that's all I needed.:cool:
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 2 ·
Replies
2
Views
7K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K