Comment by boisterousness
10 days ago
They're different. Multiplication by i gives a quarter turn counterclockwise. -i gives a quarter turn clockwise.
Opposite quarter turns cancel: (-i)(i) = (-1)(i^2) = +1
Quarter turn twice counterclockwise gives a half turn: (i)(i) = -1
Quarter turn twice clockwise also gives a half turn: (-i)(-i) = -1
Sure. Either that or the reverse. "They're not the same" in the sense that they can't both be clockwise. "They are the same" in the sense that we could make either one clockwise.