Square root of unity
= Square root of unity
{title2=$x^2=1$}
A <square root of unity> is an element $x$ of a <ring> with identity satisfying $x^2=1$. In a <field> of <characteristic> different from two, the only possibilities are $1$ and $-1$: the <difference of squares> identity $(x-1)(x+1)=0$ has no other roots because a <field> has no <zero divisors>. In a general <ring> more solutions may occur; modulo eight the four residue classes $1,3,5,7$ all have square one.