Why can't the square of radical negitive one equal to one? Unless of course, it does equal both one and negitive one, making it similar to the mathamatical avatar of the light, since light is both wave and photon...

Because nothing squared is a negative number. So the square root of a negative number is imaginary, since it can't exist.

Why can't the square of radical negitive one equal to one?

 

i²=-1 by definition.

 

Unless of course' date=' it does equal both one and negitive one,

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No, both real and complex analysis are based firmly upon excluded-middle reasoning. 1 equals 1, and it doesn't equal anything else.

Because nothing squared is a negative number. So the square root of a negative number is imaginary, since it can't exist.

 

It does exist. The appelation "imaginary" is a poor choice of terminology. Imaginary numbers aren't any more or less existant than the so-called "real" numbers.