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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

Sedumjoy
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  • 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

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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 $-2$.

The main difference is that the complex numbers don't have a good way to single out one of the two square roots as the "special" one. This contrasts sharply with the real numbers, where it is quite reasonable to single out the positive square root as the special one.

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 $i$.