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An important example of a function of a quaternion variable is
:<math>f_1(q) = u q u^{-1}</math>
which [[quaternions and spatial rotation|rotates the vector part of ''q'']] by twice the angle represented by the versor ''u''.
The quaternion [[multiplicative inverse]] <math>f_2(q) = q^{-1}</math> is another fundamental function, but as with other number systems, <math>f_2(0)</math> and related problems are generally excluded due to the nature of [[dividing by zero]].
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