GrareeCowui

2022-01-31

What are roots of unity?

lorugb

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:
${z}^{n}=1$
where $n\in \mathbb{N}$, which is to say that n is a natural number. A natural number is any positive integer: . This is sometimes referred to as a counting number and the notation for it is $\mathbb{N}$
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 $n=1$
Roots of unity: 1
When $n=2$
Roots of unity:
When $n=3$
Roots of unity
When $n=4$
Roots of unity

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