Could the fourth root of $1$ be $i$?

Question

Could the fourth root of $1$ be $i$ (or $-i$)? I could show this by doing:

1. $\sqrt[4]{1}$
2. $\sqrt{\sqrt{1}}$
3. $\sqrt{\pm{1}}$
4. $\sqrt{1}$ OR $\sqrt{-1}$
5. $\pm1$ OR $\pm i$
6. $\{1, -1, i, -i\}$

Would you include the negative square root from step 3 and include $\pm i$? Or would you simply come up with $\pm1$?

Answer 1

Precisely, no. $i$ is a fourth root of $1$, and not the fourth root of $1$.

Answer 2

1's fourth roots are indeed {1, -1, i, -i}