Roots of One

Definition

The equation

\[ x^p = 1 \]

has $p$ roots and these are called the $p$ roots of 1.¹ We call the complex numbers which solve this equation the $p$th roots of one or the ($p$th) roots of unity.

A $n$th root of unity $r \in \R $ is primitive if it is not an $m$th root of unity for any $m < n$.

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