Problem with imaginary numbers

[bugzpodder]

sqrt(x) is equilvalent x^(1/2) -- they are interchangable.
x^(1/2), exactly like sqrt(x) and every other function, gives only one answer. the definition of a function is to only have one answer. there is no such thing as one-to-many functions. for every x, you are going to get precisely one value for f(x). therefore restrictions for the domain values are often understood.

such as f(x)=sqrt(x). it is understood that x>=0.

an example of one-to-many "equation" (I can't think of a more proper term) would be like for example x^2+y^2=1
if you throw in any x, (restrictions here would be abs(x)<=1), you'll get two values for y (except when x=1), one positive, one negative. you can see by drawing a vertical line with the absolute value of x coordinate less than to 1, it'll intersect at two distinct points, thus the two y-values.

something similar to what you may have actually being talking about would be x^2, as take a look at this example:

x^2=9
abs(x)=sqrt(9)
abs(x)=3
x=3,-3

the *better* way to do the example is to do the difference of squares
x^2=9
x^2-9=0
(x-3)(x+3)=0
x=3,-3