eix = 1 + i x - x2/2! -I'm x3/3! + x4/4! + i x5/5! + …
= ( 1 - x2/2! + x4/4! + …) + i (x - x3/3! + x5/5! + …)。
Because:
cos x = 1 - x2/2! + x4/4! + …+。
sin x = x - x3/3! + x5/5! + …+。
So eix = cos x+i sin x.
On any positive spherical graph, if R is used to record the number of regions, V is used to record the number of vertices, and E is used to record the number of boundaries, then R+ V- E= 2, which is euler theorem? , it is 1640 by? Descartes first gave the proof, and then Euler independently gave the proof in 1752. We call it euler theorem, and some people abroad call it Descartes theorem.
R+ V- E= 2 is Euler's formula.