I'm pretty sure I know it's impossible....but still interesting. Considering that I explained exactly why the statement is impossible above, which has nothing to do with your reasoning, I suggest that YOU take algebra again, and maybe you will realize that equations with imaginary units are infact possible.
Actually, the logical fallacy has nothing to do with the plus/minus sign. If you want to know where the fallacy is, it lies in that when you multiply two square roots, you get the square root of the two variables under the radical sign [e.g. the square root of (a) times the square root of (b) equals the square root of (ab)] This law only applies to positive real numbers, wherein lies the fallacy.
The square root of any negative number (-x) equals the square root of that number's opposite (x) times the imaginary unit (i). The imaginary unit squared (i^2) equals negative one (-1).
