Roots Across the Complex Numbers Why is it the case that an even root (square root, quartic, etc) can be positive or negative across the complex numbers, but is limited to postive in the reals?  Is there a good mathematical reason for this, or is it simply notation?

Essentially, the reason is that complex multiplication, and by extension exponentiation, are far more complicated than in the reals.  There is a rotational aspect, and for an $n$th root, there are $n$ answers.  It would be silly to declare that only one of these is the "actual" answer, whereas in the reals it makes much more sense.  Glad to see that you have joined the site.  Please continue asking questions.
