ABSTRACT
De Moivre's theorem has several uses, including finding powers and roots of complex numbers, solving polynomial equations, calculating trigonometric identities and for evaluating the sums of trigonometric series. De Moivre's theorem has applications in electrical engineering and physics. This chapter aims to calculate powers of complex numbers and roots of complex numbers. The theorem is used to determine powers and roots of complex numbers. The theorem is also used to calculate exponential and logarithmic functions of complex numbers. There are two square roots of a real number, equal in size but opposite in sign. For example, there are three solutions to a cube root, five solutions to a fifth root and so on. In the solutions to the roots of a complex number, the modulus, is always the same, but the arguments, are different.
