i is a 90° counter-clockwise rotation

Link: http://betterexplained.com/articles/a-visual-intuitive-guide-to-imaginary-numbers/

Dude.

This guy has a pretty spiffy explanation of how complex numbers are truly happy, simple things thanks to a little bit of rotation. I shall now look for opportunities to deploy this newly-found knowledge!

Perhaps I'll play stump-the-wife. She seems like she's 90% asleep, maybe I'll finally win one. Or perhaps not.