# Is the square root of negative 1 equal to i or is it equal to plus or minus i? [duplicate]

I didn't see a duplicate.. The motivation is you tube. Tanton lectures of which one is titled " The Complex number i is NOT the square root of negative one".

Does anyone have a clue why this may be true. I did not follow his one line explanation of why the square root of negative one is plus or minus i, not i Thank you

## marked as duplicate by Hans Lundmark, Krish, Stefan4024, egreg, NamasteNov 26 '17 at 0:40

• i accepted the answer by Hurkyl just posted below but thank you for pointing out the dup I will be sure to read it! – Sedumjoy Nov 25 '17 at 16:41

The answer is that there are two square roots of $-1$.
This is no different than with real numbers; for example, there are two square roots of $4$: $2$ and $-2$.
There are ways to pick one if you need to. Various conventions are appropriate to various problems. A general one is the notion of the principal value of the square root; in the case of $-1$, its principal square root is $i$.