If we multiply by -i twice, the first multiplication would turn 1 into -i, and the second turns -i into -1. So there’s really two square roots of -1: i and -i.
This is pretty cool. We have some sort of answer, but what does it mean?
- i is a “new imaginary dimension” to measure a number
- i (or -i) is what numbers “become” when rotated
- Multiplying i is a rotation by 90 degrees counter-clockwise
- Multiplying by -i is a rotation of 90 degrees clockwise
- Two rotations in either direction is -1: it brings us back into the “regular” dimensions of positive and negative numbers.
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