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.