e to the pi times i
Permanent link to this comic: http://xkcd.com/179/
Image URL (for hotlinking/embedding): http://imgs.xkcd.com/comics/e_to_the_pi_times_i.png
{{Note my use of ^(x) and √(x) standing in for the normal maths syntax in the comic}}
[[Two people (anonymous: no hair or hats) stand in conversation, one gesturing over a flipchart of indistinct algebra.]]
EXPLAINER: NUMBERS OF THE FORM n√(-1) ARE "IMAGINARY" BUT WE CAN STILL USE THEM IN EQUATIONS.
OTHER: OKAY.
EXPLAINER: AND e^(π √(-1))=-1.
OTHER: NOW YOU'RE JUST FUCKING WITH ME.
{{alt text: I have never been totally satisfied by the explanations for why e to the ix gives a sinusoidal wave.}}