УрМатФиз / УрМатФиз с теорией

:

CI, z = 0

z = 1

! ! ! "

#

-

% !

1g = C, z

= 1

CI

I&

w0 = 0"

jzj 1

jzj

1

Im z 0 Im z 0"

( ) jzj = r * !

+1 0 + 1 0: , r ! 1 * ! ) ( ( z

2 - 1 1.

!

) ! ( 0 ' 2 "

( arg z = !

!

) "

) ! ! D1 = fz : z 2 CI

Im z 0g

D2

= fz : z 2 CI Im z 0g )

! ( ( G1 = fw : w 2CI

w 62- 1 1. w 62-1 +1.g"

)

)

! #

( (

G2 = fw : w 2CI w 62- 1 1.g:

1 1 # D = fz : z 2 CI

jzj 1

z 62- 1 1=2.

z 62-i=2 i.g ( ) . 2.7.5, .

jzj 1 -

x

= 0

1 1:

BC : y = t 1=2 t 1:

% w =

it + 1=it

=

i't2

1(

1=2 t 1

2

2t

B0 C0

)

) ) .

x = t

%

EF : y = 0

1 t 1=2 -

w =

t + 1=t

=

t2

+ 1

1 t

1=2 -

2

2t

E0 F 0

, )

) ). ,

D

G, -. -

,

. 2.7.5, .

G = fw : w 2CI w 62 5=4 1 w 62 3i=4 0:

2( 3

D =fz : z 2CI jzj 1 z 621 2 z 62 i1 i g

- . 2.7.5, .

4 jzj 1 -

x = t

1 1:

AB

:

y = 0

1 t 2: % w =

t + 1=t

=

t2 + 1

,

1 t 2

2

2t

A0 B0 ,

)

) )

w1

2 i

i=3 | w2

2 0 4i=3:

2

16

+ w3 ! "

w3

= w2

,

9

!

!

16

w3 = w22

v

9

w =

u

+ w3

t

!

!

w1 = e3= 4 3 =4 .

-

w2 = w1 + 1=w1 fw1 : w1 2CI

jw1j 1

2

Im w1 0g #$$ fw2 : w2 2 CI

Im w2

0g

% % w1 2 &i 2i' | % % ) ) w2

2

&0 3i=4':

2

9

-

* ) ) $ +$ w3 = w2 , w3 +

16

$ , , $0$ % % )

G = fw : w 2CI

Im w 0g: 1 ) ) ,

u

9

1

1

2

u

9

i2 iz + 1=z32

16

+ 4

ei3 4 z + ei3 4 z!

4

:

w = v

= v16 +

t

t

. w = v

9

+ i2 iz + 1=z32

:

u

t

16

4

2.7.5. 13 4 % G D

) 0 $ + w = z + 1=z

: 5 ) ) &z1 z2' %-

2

% ) , ,$0 z1 z2 ) -

.

1.

13 D = fz : z 2CI jzj 1 z 62&0 1' z 62&i=2 i' g6

23 D = fz : z 2CI jzj 1 Im z 0 z 62&i=2 i' g:

2.

13 D = fz : z 2CI jzj 1 z 62&1 2' z 62&i 2i' g6

23 D = fz : z 2CI jzj 1 Im z 0 z 62&i 2i' g:

3.

13 D = fz : z 2CI jzj 1 z 2 &1=2 1' z 62&i=2 i' g6

23 D = fz : z 2CI jzj 1 Im z 0 z 62& i i=2' g:

4.

13 D = fz : z 2CI jzj 1 z 62&1 +1' z 62&i 2i' g6

23 D = fz : z 2CI jzj 1 Im z 0 z 62& 2i i' g:

5.

13 D = fz : z 2CI jzj 1 z 62&1=2 1' z 62&0 i' g6

23 D = fz : z 2CI jzj 1 Re z 0 z 62&1=2 1' g: