- #1

Raparicio

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Dear Friends,

I've read about quaternions, and they can be expresed in 4 terms or in angles like this:

[tex] a + ib + jc + kd = cos \theta + \vec{v} sin \theta [/tex]

Quaternions are a generalization of the complex numbers, but in 3D. My question is about angles. For example, with a complex number, we can write:

[tex] a + ib = sin \theta + i \theta [/tex]

By generalization, is this ok?

[tex] a + ib + jc + kd = cos \theta + i sin \theta + j sin \theta + k sin \theta [/tex]

By other hand, we can take the angles in complex numbers like:

[tex] a + ib = cos \theta + i sin \theta [/tex] --> Only one angle

how much angles has a quaternion? has angle with the real part?

my best reggards.

I've read about quaternions, and they can be expresed in 4 terms or in angles like this:

[tex] a + ib + jc + kd = cos \theta + \vec{v} sin \theta [/tex]

Quaternions are a generalization of the complex numbers, but in 3D. My question is about angles. For example, with a complex number, we can write:

[tex] a + ib = sin \theta + i \theta [/tex]

By generalization, is this ok?

[tex] a + ib + jc + kd = cos \theta + i sin \theta + j sin \theta + k sin \theta [/tex]

By other hand, we can take the angles in complex numbers like:

[tex] a + ib = cos \theta + i sin \theta [/tex] --> Only one angle

how much angles has a quaternion? has angle with the real part?

my best reggards.

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