This is about math.  If you don't like math, go play with your crayons and scissors or whatever it is you people do. 

It has come to my attention through a series of failures that different math processing machines compute negative numbers raised to certain fractional exponents differently.  The math processing machines I'm talking about are my TI-86 calculator, Microsoft Excel 2003, and Matlab 2007.  This is best illustrated with the following table: 











TI-86ExcelMatlab
(-1)^(1/2)(0,1)#NUM!0.0000 + 1.0000i
(-1)^(1/3)-1-10.5000 + 0.8660i
(-1)^(2/3)1#NUM!-0.5000 + 0.8660i
The TI-86 seems to be the only one that's consistently correct.  The notation "(0,1)" indicates an imaginary number, which is correct, and the 2/3 exponent is calculated as if it were entered [(-1)^(1/3)]^2, which is how it's supposed to be done.  For some reason, Excel doesn't calculate powers this way, so it doesn't properly calculate the 2/3 exponent.  But if you enter the formula as [(-1)^(1/3)]^2, Excel figures it out properly.  Finally, Matlab does its own thing in its own little world.  It renders each result as imaginary, even though only certain exponents yield an imaginary component. 

To avoid overstating the issue, let me assure you the pattern continues.  In fact, the pattern is as follows: 
(x)^(y/z) is real for all negative real x, all positive whole y, and all positive whole odd z
If any of those conditions isn't met, the result will be imaginary, which isn't necessarily a bad thing, but after a brief five-year career in engineering, I still haven't discovered the purpose of imaginary numbers. 

Echoing what I found, SparkNotes says, "Since we cannot take the even root of a negative number, we cannot take a negative number to a fractional power if the denominator of the exponent is even."  This is because any fraction with an even denominator can be broken down into [something] × 1/2, which yields an imaginary result. #math