# Imaginary fun

#### Mark44

Joined Nov 26, 2007
628
Recca,
That's the step that's causing problems, converting a square root of a quotient into the quotient of the square roots. That's valid only if the numerator is nonnegative and the denominator is positive.

Concerning the square root function, f(x) = $$\sqrt{x}$$, and as noted elsewhere in this thread, this is generally understood by mathematicians to be a single-valued function, with domain and range being the nonnegative reals. It's possible to extend the domain to negative reals, but then the range is no longer a subset of the reals.

Mark