Q81Section C (Part C)81 of 120

Contour integral of $e^ze^{1/z}$ around the unit circle

Let $\gamma:[0,1]\to\mathbb C$ be the function $t\mapsto e^{2\pi it}$ and

$I=\int_\gamma e^{z}e^{\frac1z}\,dz.$

Which of the following statements are true?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

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