now multiply by some other complex number ##a_2 + b_2 i## and see that
##\big(a_1 \mathbf I + b_1 \mathbf i\big)\big(a_2 \mathbf I + b_2 \mathbf i\big) = \big(a_2 \mathbf I + b_2 \mathbf i\big) \big(a_1 \mathbf I + b_1 \mathbf i\big) ##
because ##\mathbf i## commutes with scaled forms of itself and the identity matrix ##\mathbf I## commutes with everything. Since you are talking about rotation matrices, you are constraining yourself to a determinant of 1 here (aka complex numbers on the unit circle).
- - - - - edit: cleaned up some table formatting issues based on below hint
This was created by PF5, it "thought" you were making a table, so it wrapped TABLE HTML tags around the area.
New feature. If you get them and do not want them, toogle into bbcode (gear-like icon on the toolbar, far right).
Remove the two tags - most HTML tags have start and end like this [STARTME] ....blah blah [/STARTME].
You can do this on your next post, I think the one post above is old enough to have locked you out of edit. If you want I can clean them up, PM me.
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