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Unformatted text preview: . Consider f (z ) = ez . Find all the points where f is analytic. 6 (10 points) 5. Use Cauchy’s formula to prove that if f is entire, then for any R > 0,
2π
1
f (Reit )dt .
f (0) =
2π 0 7 (10 points) 6. Calculate the Laurent series for the function f (z ) =
√
annulus 2 < z  < 2. 8 1
2+z 2 1
+ 2−z and z in the (15 points) 7. Find all the solutions of the equation sin(z ) = cos(z ) and express them in
terms of the (multivalued) logarithm of suitable complex numbers. 9 [(15 points) 8.] Power and Taylor series
(a) (5 points) Find the radius of convergence of the power series
∞
1
zj
2
j
j =1 (b) (10 points) Given that
∞
1
=
wj
1−w
j =0
for w < 1, ﬁnd the Maclaurin series fo...
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This note was uploaded on 01/21/2014 for the course MATH 3364 taught by Professor Staff during the Fall '08 term at University of Houston.
 Fall '08
 Staff
 Math

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