The square root of negative one is an imaginary number named i. I presume most you already know that. One of the most famous results in all of mathematics is this little fact about some of our favorite constants:
eiπ = -1
Here's a lesser known but equally stunning little fact about our friend: ii has a real numbered answer (well, infinitely many, if you want to be technical about it, but I'm going to skirt that issue.) Yes, it's true. ii equals about 0.2. Ask google. See for yourself.
It’s fairly trivial to show, actually:
eiπ = -1 |
Euler's Identity |
e½iπ = i |
take the square root of both sides. |
e½(i*i)π = ii |
raise both sides to the ith power. |
e-½π = ii |
because i*i = -1 |