What are roots of unity?

Step 1
A root of unity is a complex number that when raised to some positive integer will return 1.
It is any complex number z which satisfies the following equation:
${\displaystyle z^n=1}$
where ${\displaystyle n\in \mathbb{N}}$, which is to say that n is a natural number. A natural number is any positive integer: ${\displaystyle (n=1,2,3,\cdots )}$. This is sometimes referred to as a counting number and the notation for it is ${\displaystyle \mathbb{N}}$
For any n, there may be multiple z values that satisfy that equation, and those values comprise the roots of unity for that n.
When ${\displaystyle n=1}$
Roots of unity: 1
When ${\displaystyle n=2}$
Roots of unity: ${\displaystyle -1,1}$
When ${\displaystyle n=3}$
Roots of unity ${\displaystyle =1,\frac{1+\sqrt{3}i}{2},\frac{1-\sqrt{3}i}{2}}$
When ${\displaystyle n=4}$
Roots of unity ${\displaystyle =1,i,1,-i}$