Hi singleton. I've used both Maple and Mathematica (althoug not Calculus Wiz) and I would say that at the calculus level there isn't much difference.
Say, you need to check the derivative of something, and the integral of some other function? Both will do the trick.
In Mathematica (the...
Your problem seems to be
i^4 =i^0 \quad /()^{\frac{1}{2}}
i^2 \neq i^0
Well, the thing is that one has to be more careful when dealing with complex numbers, and specially with complex functions. In any case
(i^4) ^{\frac{1}{2}}^=1
That's because when dealing with complex numbers...
Using synthetic div I got
\frac{-33}{2-x}+(19 + 12 x + 2 x^2 + 3 x^3)
I think you're using the same method. If so, you should multiply by 2. Remember that when dividing by x-c you multiply by c.
Nonsense.
It's customary to extend functions by means of continuity to points where it isn't defined.
For instance, x \sin \frac{1}{x}} is defined as equals to 0 at x=0 by continuity. That doesn't mean that I'm defining 1/x in the set of Real numbers, I'm defining the whole function.