Past exam of the mathematical methods I course of the University of Oxford / 2013 / 10 / a / Solution

De Moivre's theorem states that, for real $\theta$ and integer $n$,It follows from $\cos \theta +i\sin \theta =e^{i\theta }$ and exponent multiplication. Negative integers are allowed because this unit-modulus complex number is nonzero. For a general polar number $r{e}^{i\theta }$, its integer power also has the factor $r^n$.