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I don't think I quite followed the step where he/she writes "i^4 = 1", where they are relating rotation and the natural numbers. The RHS is theoretically the co
by luser001 14y ago
I don't think I quite followed the step where he/she writes "i^4 = 1", where they are relating rotation and the natural numbers. The RHS is theoretically the concept "identity under rotation". Why should it be be the same as the natural number 1?
Maybe I missed something in the explanation. Can somebody explain?
- T-hawk 14y agoThere is an implicit start from the unit vector 1. i (really 1 * i) is a 90° rotation of that. i^4 is four 90° rotations. Rotate anything four times and you've rotated it 360°, ending up where you started at 1.
- luser001 14y agoOk, thx. I think I understand now.
- irishcoffee 14y ago* i = sqrt(-1) * i * i = i^2 = sqrt(-1) * sqrt(-1) = -1 .. i^4 = i^2 * i^2 = -1 * -1 = 1