I was wondering if there was an extension of Euler's Identity to quaternions. Now, in two dimensions, there is only one direction of rotation. In three dimensions, there are two,"axes", of rotation. Therefore, the formula that I would like needs three different values of theta for rotation. Is there any such formula? Notice: The other formulas that were provided on this site are based on one angle of theta and a quaternion rotation on the angle theta. However, since four-dimensional space has three axes of rotation, the formula provided should have three values of theta.
2026-03-29 13:27:17.1774790837
On the creation of a formula of Euler's Identity for quaternions
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