(cos x + ix)n = cos(nx) + i sin (nx).
The formula is important because it connects complex numbers (i stands for the imaginary unit) and trigonometry. The expression cos x + i sin x is sometimes abbreviated cis x.
By expanding the left hand side and then comparing the real and imaginary parts under the assumption that x is real, it is possible to derive useful expressions for cos (nx) and sin (nx) in terms of cos x and sin x. Furthermore, one can use a generalization of this formula to find explicit expressions for the nth roots of unity, that is, complex numbers z such that zn = 1.