Residue of $\dfrac{z^{1/4}}{z+1}$ at $ z = -1$. This question is from Churchill and Brown's Complex Variables and Applications 8th edition, page 248: 

Find $Res ({f},-1)  $ for $f = \dfrac{z^{1/4}}{z+1}$ given $|z| > 0, 0 < \arg z< 2\pi$

Attempt: 
Since the denominator has a simple zero, the residue is $(-1)^{1/4}$. Now, this has four values: $e^{i\pi\left(\frac{1+2n}{4}\right)}$ for $n = 0,1,2,3$. How to decide which value I should choose? 

Feels like the function $f$ you are using is not specified sufficiently. In other words you would have have the same problem evaluating $f(2)$, for example.
So for example, if the idea behind $f$ is to use the smallest positive angle, then you would apply the same principle to computing the residue, choosing $n=0$.
