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How to Add Quaternions

Quaternions are part of a four-dimensional numbering system that implements complex numbers into its calculations. Quaternions are commonly used to represent the three-dimensional rotation of an object. A quaternion has one real-number dimension and three imaginary-number dimensions. An imaginary number is one that's negative when it's squared: i^2 = -1. A squared real number is never negative. Quaternions can be added together in a way similar to that of adding real numbers, with the difference being the presence of imaginary numbers within the expression.

Instructions

- 1
  Separate the real and imaginary terms in the quaternions and add them independently. For example, adding the general quaternion (a + b(i) + c(j) + d(k)) + (A + B(i) + C(j) + D(k)), where a and A are real numbers and b, B, c, C, d and D are imaginary numbers, separates like so: (a + A) + (b + B)i + (c + C)j + (d + D)k.
- 2
  Add the components within parentheses together as indicated in the newly formed expression.
- 3
  Simplify the expression by multiplying the sums by their imaginary components, except for the term in the quaternion that has no imaginary component but is the sum of two real numbers.

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