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Multiplication of quaternions

  1. Apr 9, 2007 #1
    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)

    Justify your response.

    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. jcsd
  3. Apr 9, 2007 #2


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    Staff Emeritus
    Science Advisor

    Isn't that how multiplication of the quaternions is defined?
    Last edited: Apr 9, 2007
  4. Apr 9, 2007 #3

    D H

    Staff: Mentor

    It works necessarily because quaternion multiplication distributes over quaternion addition per the definitions of quaternion multiplication and addition.
  5. Apr 9, 2007 #4
    Thanks guys, thats all I needed.:cool:
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