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I would like to learn about Quaternions. I've read this article: https://en.wikipedia.org/wiki/Quaternion

Most of the article was not hard to understand, except the (Exponential, logarithm, and power) part.

To calculate the exponential, I have to calculate sin/cos of the imaginary part, but that functions aren't defined on Quaternions (in the article).

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As you can see in the answer cited in the comment, the exponential of a quaternion $z=a+b\mathbf{i}+c\mathbf{j}+d\mathbf{k} = a+\mathbf{v}$, is:

$$ e^z = e^{a+\mathbf{v}}=e^a \left( \cos |\mathbf{v}| +\dfrac{\mathbf{v}}{|\mathbf{v}|} \,\sin |\mathbf{v}| \right) $$

where $|\mathbf v|= \sqrt{b^2+c^2+d^2}$ is a real number (the modulus of $\mathbf v$), so $\cos |\mathbf{v}|$ and $ \sin |\mathbf{v}|$ are well known trigonometric function of a real number, and they have nothing to do with $\cos$ and $\sin$ of a quaternion.

Such ''trigonometric function'' of a quaternion can be defined using a series expansion, in an analogous way than the exponential function because also these series are absolutely convergent, but non commutativity of quaternions gives some troubles about the properties of such functions.

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