This xkcd reminds me of an old story. Kyle and I were at Sequoia Natl park, hiking through the trees and discussing science, math, and other sundries. At some point I said something which ended with the justification, "because e to the i 2 pi is one," and he almost laughed at me. Come on!
But when you use euler's formula, well, it's right there. So easy.
I love that.
So I justified it to Kyle on a little scrap of paper in my pocket... and for the rest of the afternoon we would shout it every once in awhile to the skies-- e to the i 2 pi is ONE!!!