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I have 2 Quaternion equations and I'm trying to find material on how to solve them:

1 = 2 − + + 3

2 = −1 + + 4 − 2

I need to find the difference of the 2 sums and the Quaternion Product.

I've literally searched everywhere and can't find decent material that can help me solve these equations and get the properties I need.

I'm not asking for anyone to solve these equations I'm simply asking if anyone could direct me to some material that can help me get the properties I need (as I need to write a program that solves these too) or if anyone would care to explain in some detail how I can go about solving these?

Thanks in advance!

[EDIT]

Here's the question I've been asked in full:

Given the following two quaternions equations:

1 = 2 − + + 3

2 = −1 + + 4 − 2

Where (i, j, k) belong in the Imaginary Space: Calculate analytically the following series of properties: • Sum and difference of the two quaternions • Quaternions product

Open Source
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  • Not sure what you mean by "difference of the 2 sums." Can you elaborate? For the product, do you know how to multiply $1, i, j, k$ with each other? Also, note that quaternion multiplication is not commutative, so you need to specify the order in which you wish to multiply: $q_1q_2$ or $q_2 q_1$. –  Mar 22 '18 at 14:53
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    Could you write down the explicit equations you want to solve? – Dietrich Burde Mar 22 '18 at 14:53
  • I've just updated my question providing the full information – Open Source Mar 22 '18 at 14:55
  • And no @Bungo I'm not sure I know how to multiply i,j k. Also I'd multiple q1,q2 – Open Source Mar 22 '18 at 14:58
  • Equations 22 and 23 at mathworld.wolfram.com/Quaternion.html should be helpful. –  Mar 22 '18 at 15:01
  • This looks great, I'll have a look at this tonight, thank you @Bungo. – Open Source Mar 22 '18 at 15:23
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    Those are not "equations". It is just labeling two quaternions (and for no apparent purpose, since it didn't make any use of the labels afterwards). All you have to do is add them, subtract them, and multipy them. Surely wherever you found this problem also defined addition, subtraction, and multiplication of quaternions, did they not? Addition and subtraction are very easy. Multiplication is straightforward, but time-consuming. – Paul Sinclair Mar 23 '18 at 00:06

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