Problem 9

Let $\theta\in\mathbb{R}$. De Moivre’s formula states that

for all non-negative integers $n$.

1. Prove De Moivre’s formula.(Hint: you will need an exercise given elsewhere in the book and an exercise given elsewhere in the book.)

2. Deduce a primitive $n$th root of unity in $\mathbb{C}$, proving your answer.