/sci/ - Science & Math

>>8886797
So this is the expansion of e^x derived by using the equation in the previous post. Now instead of x, put in (i*x) for x, for the definition of i that you know, i^2 = -1, i^3 = -i, i^4 = 1

So some of the terms become negative and some still have i's in them and some terms have both. Now if you look at the sin x and cos x expansions, combined they form the expansion for e^x, and all of the sin terms would still have an i attached to them, and the i can be factored out, so that the equation forms e^ix = cos (x) + i*sin (x)

Instert pi into the eq, and it works