(Solution) 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)... > Snapessays.com

(Solution) 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)...

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

)

|

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This question was answered on: Sep 21, 2023

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Sep 21, 2023

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