is nthroot of a negative number imaginary if n is not whole number I wanted to find the domain of a function which is defined as $y=x^{1/x}$
For negative $x$, if $x$ is even then the result will be imaginary, if $x$ is odd then the result is real. However, what about $x=-2.5$ or $-e$?
The n-th root of a number is that number raised to the power  1/n. So the 1/3-th root of a number is just that number cubed. Thus, by these definitions, the 1/3-th root of -5 is -125, which is not imaginary. Or did I misunderstand the question?
The n-th root of a number is that number raised to the power  1/n. So the 1/3-th root of a number is just that number cubed. Thus, by these definitions, the 1/3-th root of -5 is -125, which is not imaginary. Or did I misunderstand the question?