De Moivre's formula

Theorem: (cos x + i sin x)^n = cos nx + i sin nx

In mathematics, de Moivre's formula (also known as de Moivre's theorem and de Moivre's identity) states that for any real number x and integer n, ( cos ⁡ x + i sin ⁡ x) n = cos ⁡ n x + i sin ⁡ n x , {\displaystyle {\big (}\cos x+i\sin x{\big)}^{n}=\cos nx+i\sin nx,} where i is the imaginary unit (i2 = −1). The formula is named after Abraham de Moivre, although he never stated it in his works. The expression cos x + i sin x is sometimes abbreviated to cis x.

From Wikipedia, under CC BY-SA. More on occurri.