Overview
Show that every quaternion ? P H can be written in polar form as ? “ |?|pcos ?`u sin ?q, where u is imaginary of length 1.
Suppose that ? “ cos ? ` u sin ? where u is imaginary of length 1, and let x be any imaginary quaternion. Recall that we can also think of u and x as vectors in R 3 . Explain why ? ´1x? corresponds to the rotation of x around the axis u by angle 2?
Consider the following set of 24 quaternions: t?1, ?i, ?j, ?k,p?1?i?j?kq{2u. Explain how this set is related to a regular tetrahedron. [Hint: A regular tetrahedron has 12 rotational symmetries.] http://www.zipcon.net/~swhite/docs/math/quaternions/geometry.htmlhttps://math.stackexchange.com/questions/1496308/h...might be helpful