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Question

The contour integral ce1/zdz with C as the counter clock wise unit circle in the z-plnae is equal to

A
0
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B
2π
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C
2π1
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D
α
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Solution

The correct option is C 2π1
The Laurent Expansion in the negihbourhood of z=0 is given as
f(z)=e1z=1+11z+12!z2+13!z3+....
So, R1=Resf(z);(z=0)
= Coefficient of 1Z in Laurent expansion
So by Cauchy residue theorem
e1zdz=2πi(R1)=2πi(1)=2π1

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