Question

What is De Moiver'sTheorem?
And what are the related equations/theorems?

Answer 1

$$\begin{gathered} \mathrm{De}\mathrm{Moiver}\text{'}\mathrm{s}\mathrm{theorem}\mathrm{states}\mathrm{that}\mathrm{for}\mathrm{complex}\mathrm{number}\mathrm{and}\mathrm{integer},\mathrm{n} \\ {\left(\cos \mathrm{x}+\mathrm{i}\sin \mathrm{x}\right)}^{\mathrm{n}}=\cos \mathrm{nx}+\mathrm{i}\sin \mathrm{nx} \\ {\left({\mathrm{e}}^{\mathrm{i\theta }}\right)}^{\mathrm{n}}={\mathrm{e}}^{\mathrm{in\theta }} \end{gathered}$$