Coding Games and Programming Challenges to Code Better
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Here’s another post-hoc feedback. Sorry it doesn’t come before submission, I got sidetracked on other problems and figured since this one was by TheNinja it shouldn’t need too much review 
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it’s spelled “quaternion” (from latin numerus iterativum quater, “four”), not “quarternion”). Sprinkled all over the puzzle including title.
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I don’t use them everyday, but when I did the real part came first, not last. The inversion is correctly specified in the problem, yet surprising. They’re a basis, not a linear equation set!
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That said, cool problem, I like it!
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I’m oddly satisfied that zero handling wasn’t needed at all.
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Suggestion: remove parentheses where not needed in the example multiplication, since they’re not only not needed in the expected output but actually forbidden there.