As the video on http://www.youtube.com/watch?v=2kbM96Jr4nk
It says that: $1\cdot(-1)=-1$ can represent as $1$ rotated $180^{\circ}$ around the Origin to get $-1$
$$1\cdot(-1)\mapsto 1\quad\text{Rotate}(180 ^{\circ})$$ so it must be:
$$1\cdot\sqrt{-1}\mapsto 1\quad\text{Rotate}(90 ^{\circ})$$
but how to map: $$(-1\rightarrow\sqrt{-1}\ )\mapsto (180 ^{\circ}\rightarrow90^{\circ}) $$ Is there any principles to map the two transforms, or it's just a basic define as $1+1=2$.