De Moivre's Formula

Formula: $$\left(\cos x+i\sin x\right)^n=\cos\left(nx\right)+i\sin\left(nx\right).\,$$

The formula can be derived from Euler's formula,


 * $$e^{ix} = \cos x + i\sin x\,$$

and laws of exponentials,


 * $$\left( e^{ix} \right)^n = e^{inx} .\,$$

Then, by Euler's formula,


 * $$e^{i(nx)} = \cos(nx) + i\sin(nx)\,$$.