Complex Numbers HL - de Moivre's Theorem
De Moivre's Theorem gives a formula for calculating complex numbers. It enables us to connect complex numbers and trigonometry. Most importantly, it is incredibly useful for finding powers and roots of complex numbers. It can be stated in a number of ways: [r(\cos\theta+i\sin\theta)]^n=r^n(\cos(n\theta)+i\sin(n\theta)) Whilst we can prove the formula using proof by induction, it becomes clear when we write it in...