De Moivre’s theorem is a fundamental result in complex numbers that connects powers of complex numbers to trigonometry. It states that if you take a complex number in polar form, written as cos(θ) i·sin(θ), and raise it to the power n, the result is cos(nθ) i·sin(nθ). This relationship makes it very easy to work with powers and roots of complex numbers, since multiplying a complex number by itself n times just multiplies the angle by n. The theorem shows the deep link between algebra and trigono