Perfection

z = cos x + i·sin x

dz/dx = -sin x + i·cos x

dz/dx = i ( i·sin x + cos x ) (i² = -1)

dz/dx = i·z

dz/z = i·dx

ln|z| = i·x

z = e ͥ ͯ

e ͥ ͯ = cos x + i·sin x

... substitute x for π...

Done