Title: 10_4 De Moivre’s Theorem
Course: HELM Workbooks 2023-2024 > Section: HELM 10: Complex Numbers

In this Section we introduce De Moivre’s theorem and examine some of its consequences. We shall see that one of its uses is in obtaining relationships between trigonometric functions of multiple angles (like \(\sin 3x,\) \(\cos 7x\)) and powers of trigonometric functions (like \(\sin ^2x\), \(\cos^4x\)). Another important use of De Moivre’s theorem is in obtaining complex roots of polynomial equations. In this application we re-examine our definition of the argument arg\((z)\) of a complex number.