Due to a math problem set, I have absolutely no time to write a lengthy post today. But I’ll share what really rattled my mind in high school:
My first thought was that this identity doesn’t make sense. How can you take e to an imaginary power?
Anyways, the fun part is staring at it and appreciating all the elements involved here in their elegant simplicity:
i – an imaginary number
1 – the identity in multiplication
0 – the identity in addition
pi – the commonly used irrational number
e – the commonly used transcendental number
Now the not-so-fun part is proving it (from the power series definition of e^x). Good luck with that.
P.S. Actually both pi and e are transcendental.