# Multiplication of quaternions

1. Apr 9, 2007

### flash

1. The problem statement, all variables and given/known data
Expand and simplify the product of two quaternions:

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

3. 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?

2. Apr 9, 2007

### cristo

Staff Emeritus
Isn't that how multiplication of the quaternions is defined?

Last edited: Apr 9, 2007
3. Apr 9, 2007

### D H

Staff Emeritus
It works necessarily because quaternion multiplication distributes over quaternion addition per the definitions of quaternion multiplication and addition.

4. Apr 9, 2007

### flash

Thanks guys, thats all I needed.