De Moivre’s Theorem #
Statement:
- \( \bf \left(\cos\theta+i\sin\theta\right)^{n}=\cos n\theta+i\sin n\theta \) when \(\bf n\in \Z \)
- \(\bf \cos n\theta+i\sin n\theta \) is one of the value of \( \bf \left(\cos\theta+i\sin\theta\right)^{n}\) when \(\bf n=\frac{p}{q} \) where \(\bf q\ne 1 \)
Proof:\( \\ \)