Any ideas on how to approach this kind of question?? What does the question means I for each of the branches??
2026-03-26 18:56:39.1774551399
contour integral and branch cut question
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With the branch cut along the positive real axis, we have
$$z^{1/5}=R^{1/5}e^{i\phi/5}e^{i2n\pi/5}$$
for $n=0,1,2,3,4$. The index $n$ defines the branches.
Hence, we have
$$I_n=-R^{6/5}e^{i2n\pi/5}\int_0^{2\pi} e^{i6\phi/5}\,d\phi$$
Can you finish now?