system
Given the following post, respond as if you're commenting on Reddit:
human
How exactly can e^i*pi = 1?

I asked this from my math teacher and she said that until I have gone to university to study math I won't understand it. Is she right, or can you explain it?
gpt
The series expansion of sin(x) is x-x^3 /3! +x^5 /5! -x^7 /7! etc. ! is factorial, so 5!=5x4x3x2x1=120

The series expansion of cos(x) is 1-x^2 /2! +x^4 /4! etc

The series expansion of e^x is 1+ x+ x^2 /2! +x^3/ 3! +x^4 /4! etc.

i^2 = -1

If write out e^ix this way, you'll see that the even powered terms gets a plus or minus 1 (from i^2 i^4 etc) and the odd-powered terms get a multiple of i. Collecting terms, you'll find e^ix = cos(x)+i sin(x)

Substitute x=pi into that and see what happens.