Question 1 a,b,c,d. Complex Analysis..................................................AMath / PMath 332 - Assignment 03 (Due Friday May 27, 12:00 noon)
1. Write any
z
?
C
as
z
=
x
+
iy
. Write any complex function as
f
(
x
+
iy
) =
u
(
x,y
)+
iv
(
x,y
).
Write a particular complex number of interest as
z
=
x
+
iy
. Throughout this question
you will be analyze the equation
lim
z
?
z
f
(
z
) =
lim
(
x,y
)
?
(
x
,y
)
u
(
x,y
) +
i
lim
(
x,y
)
?
(
x
,y
)
v
(
x,y
)
(1)
De?nition 1
We say that
lim
(
x,y
)
?
(
x
,y
)
u
(
x,y
)
exists, and
lim
(
x,y
)
?
(
x
,y
)
u
(
x,y
) =
a
, for some
a
?
R
if, for any
± >
, there exists a
? >
such that whenever
|
(
x,y
)
-
(
x
,y
)
|
This question was answered on: Sep 21, 2023
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