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:

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

$i$ is a fourth root of $1$, yes. – littleO Apr 09 '14 at 00:38 — littleO, Apr 09 '14 at 00:38
Yes..... $i \times i \times i \times i = -1 \times -1 = 1$ – barak manos Apr 09 '14 at 00:41 — barak manos, Apr 09 '14 at 00:41

score 1 · Accepted Answer · answered Apr 09 '14 at 00:45

1

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

answered Apr 09 '14 at 00:45

Ugo Iaba

score 0 · Answer 2 · answered Apr 09 '14 at 00:39

0

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

answered Apr 09 '14 at 00:39

Jonathan Hebert

2 Answers2