How do you verify euler's formula?

Answer 1

Euler's formula refers to a formula in complex analysis that links trigonometric function with the complex exponential function. It states that, for any real number x,

eix = cos(x) + i*sin(x) where

i is the imaginary square root of -1, and the angle x is measured in radians.

That formula is not easy to verify.

However, it is quite possible that what the questioner calls the Euler formula is actually a reference to the Euler characteristic. In its basic form, it states that for any convex polyhedron, the numbers of vertices (V), edges (E) and faces (F) are related by

V - E + F = 2

Verification in the case of basic polyhedra is simple but general verification is not simple. See the link below.