Question

What is the De Moivre’s Theorem?

Answer

If n be an integer, then${\left(\mathrm{cos\theta }+i\mathrm{ sin\theta }\right)}^n=\cos n\theta +i\sin n\theta$and if n be a rational number$\mathrm{i.e. }n=\frac{p}{q},p,q ϵ z,q\ne 0, \mathrm{then\; cos}\left(p^{\theta }/q\right)+i\sin \left(p^{\theta }q\right)\text{is one of the values of}{\left(\mathrm{cos\; \theta }+i\mathrm{sin\; \theta }\right)}^{p/q}$