# contour integral and branch cut question

Any ideas on how to approach this kind of question?? What does the question means I for each of the branches??

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?

• hi @Mark Viola , thanks for helping...can I say that even though the diagram drew the circle in the sense it passes through the branch cut but actually it doesn't right?? Commented Nov 16, 2017 at 16:13
• Also I don't have to solve the contour like the one shown in the link??? upload.wikimedia.org/wikipedia/commons/thumb/8/8d/… Commented Nov 16, 2017 at 16:14
• You're welcome. My pleasure. Commented Nov 16, 2017 at 17:26
• The contour begins at $\pi =2\pi ^-$ and ends at $\phi =0^+$. Commented Nov 16, 2017 at 17:27
• I'm not sure as to your meaning of "solve the contour like the one shown in the link." Commented Nov 16, 2017 at 17:29