Expanding Using De Moivre's Theorem

De Moivre's Theorem is a notable formula utilized in the complex number algebra realm, serving as a bridge between the fields of trigonometry and complex exponentials. The theorem posits that for any given real number x and integer n, the equation (cos x + i sin x)^n equates to cos nx + i sin nx. This theorem is incredibly useful in the expansion of complex numbers when they are raised to a power.