Recall that quarternions are like complex numbers on steroids. They have three imaginary units i, j, k each of which squares to minus one, just like the complex unit:
i² = -1
To get dual quarternions, take two quarternions A and B and think of one of them as carrying a new kind of symbol ε:
ε also reacts in a funny way when squared:
ε² = 0
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