M417
Fall 1996
hw4.tex due September 25, 1996
1.
Find
dtan
−1
z
dz
2.
a)
Find a [multivalued] function F
+
(z) such that [(dF
+
)/dz] = [1/(1 + i z)].
b)
Find a [multivalued] function F
−
(z) such that [(dF
−
)/dz] = [1/(1 − i z)].
3.
Show that
1
1 + z
2
=
1
2
⎧
⎨
⎩
1
1 + i z
+
1
1 − i z
⎫
⎬
⎭
.
4.
Find a (single valued!) function F(z) defined in the strip
{−1 < ℑz < 1 }
such that
•
F(z) is analytic (single valued!),
•
[dF /dz] = [1 /(1 + z
2
)],
•
F(0) = π.
What is F(1)?
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X by
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T
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, version 4.06.
On 06 Feb 2017, 13:07.