1. The problem asks for the square roots of 1. 2. By definition, a square root of a number $a$ is a number $x$ such that $x^2 = a$. 3. We want to find all $x$ such that $x^2 = 1$. 4. Solve the equation: $$x^2 = 1$$ 5. This can be rewritten as: $$x^2 - 1 = 0$$ 6. Factor the left side using the difference of squares: $$ (x - 1)(x + 1) = 0 $$ 7. Set each factor equal to zero: $$x - 1 = 0 \implies x = 1$$ $$x + 1 = 0 \implies x = -1$$ 8. Therefore, the square roots of 1 are $1$ and $-1$. 9. The other options $i$ and $-i$ satisfy $x^2 = -1$, not $1$. Final answer: The square roots of 1 are $1$ and $-1$.