УрМатФиз / УрМатФиз с теорией

z z2

:

z z3

:

2:7:1

z1 z2

z1 z3

z 0

z 1

w + 2 w 0

:

=

:

:

i 0

i 1

1 + 2

1 0

w + 2

z

2

= i

, w =

:

w

iz 1

. w = 2= iz 1:

) * $' #

' # +

$ $ z, z1, z2, z3 2.7.1 :

z + i

: z

1

=

w 0

:

w 2

z + i =

2w

w =

2z + i

:

,

w 2 ,

0 + i

0

1

2 0

2 2

i

z i

z 0

:

z 1

= w w2

: w + w2

,

z =

w w2w2

,

w=w2 z + 1

:

1 0

1

1

p

0 w2

0 + w2

w2w + w2

1 z

z + 1

2 1 + i

w =

2

1

z:

6. 1 D = fz : z 2CI Im z 2g G = fw : w 2CI

jwj 2g

w 2i = 2 w 4i = 0:

2 D = fz : z 2CI Re z 0 Im z 0g

G = fw : w 2CI jwj 2 Re w 0g

w 1 = 0 w 0 = 2i:

2 D = fz : z 2CI Re z 0 Im z 0g

G = w : w

CI

w 4 Re w

Im w

w 1f = 0

2w 0 j=j2p

1 + i :

g

2

9. 1 D = fz : z 2CI

jzj 2g G = fw : w

2CI Re w 1g

w 0 = 2 w 2 = 1:

2 D = fz : z 2CI Re z 0 Im z 0g

G = fw : w

2CI

jwj 5 Re w Im wg

w i = 0 w 0 = 5p

1 i =2:

2

10. 1 D = fz : z

2CI

jzj 2g G = fw : w 2CI

Im w 3g

w 1 = 6i w 2i = 3i:

2 D = fz : z

2CI Re z 0 Im z 0g

G = fw : w 2CI

jwj 1 Re w Im wg

w 1 = 0 w 0 = p

1 + i =2:

2

11. 1 D = fz : z

2CI

Im z 3g

G = fw : w

2CI

jwj 2g

w 3i = 2 w 6i = 0:

2 D = fz : z

2CI Re z 0 Im z 0g

G = fw : w 2CI

jwj 2 Re w 0g

w i = 0 w 0 = 2i:

12. 1 D = fz : z

2CI

Re z 2g

G = fw : w

2CI

jwj 3g

w 2 = 3i w 4 = 0:

2 D = fz : z

2CI Re z 0 Im z 0g

G = fw : w 2CI

jwj 3 Im w 0g

w 1 = 0 w 0 = 3:

13. 1 D = fz : z

2CI

jzj 3g G = fw : w 2CI

Im w 4g

w 0 = 8i w 3 = 4i:

2 D = fz : z

2CI Re z 0 Im z 0g

G = fw : w 2CI

jwj 4 Re w 0g

w 1 = 0 w 0 = 4i:

25. 1 D = fz : z 2CI

jzj 3g G = fw : w 2CI

Im w 4g

w 1 = 0 w 3i = 4i:

2 D = fz : z 2CI Re z 0 Im z 0g

G = fw : w 2CI

jwj 1 Re w Im wg

w 1 = 0 w 0 = p

1 + i =2:

2

26. 1 D = fz : z 2CI

Im z 1g G = fw : w

2CI jwj 1g

w i = 1 w 0 = 0:

2 D = fz : z 2CI Re z 0 Im z 0g

G = fw : w 2CI

jwj 1 Im w Re wg

w i = 0 w 0 = p

1 + i =2:

2

27. 1 D = fz : z 2CI

Re z 2g G = fw : w

2CI

jwj 1g

w 2 = 1 w 0 = 1:

2 D = fz : z 2CI Re z 0 Im z 0g

G = fw : w 2CI

jwj 1 Im w 0g

w i = 0 w 0 = 1:

28. 1 D = fz : z 2CI

jzj 1g G = fw : w 2CI

Re w 1g

w 1 = 1 w 1 = 2:

2 D = fz : z 2CI

Re z 0 Im z 0g

G = fw : w 2CI

jwj 1 Re w 0g

w 1 = 0 w 0 = i:

2 D = fz : z

2CI Re z 0 Im z 0g

G = fw : w 2CI

jwj 2 Im w 0g

w 1 = 0

w 0 = 2:

2.7.3. - w = wz

D

G=fw : w 2CI Im w 0g:

1

D =

f

z

: z

2

CI

Re z 0 z

i i + 2 z

3 + i +

1

+ i

g

"

62

62

2

D =

f

z

: z

2

CI

z

z

= 1

Im z

Re z

0

gg

:

62jfj

. #$ $ % % w = zn, n 2N' ( $ $(

) ) :

$ $ % % ( * +

+

) ,$ -

I-

CI

f1g"

$ C

=

% (

%) % %

%

Dk =

z : z 2CI

2 k

2 k + 1

k

arg z

= 0 n

1: . ( % * $ Dk -

n

n

$%

*$* $ ($)$

G =

f

w : w

2

CI

w

0

1 g

$ + / )$ * +$ $

/$

62

arg z 2 "

$($ $0 ) $($ 1 0

D0 = fz : z

2CI

Im z 0g

D1 = fz : z

2CI

Im z 0g

-

*$*

$

($)$

G =

f

w

: w

2

w

0

1 g

: # )$ )$ ( * + % -

CI

62

2

$) % )$) ) ( / % z

=

p

= q w

ei arg w=2

w

G D0,

j j

2

z =

pw =

= q

jwj

ei arg w+2 =2

G D1:

1

w1 = z

i w2 = z i 2

w2

9

w3 =

w =

pw3

. 2.7.3, , "

2

w2

4

# $

p

2

w1 = z i

w2 = z i 2

. 2.7.3,

2v

. w =

z i 2 9:

u

z i

4

t

2

2

- , -

z

= 1

"

Im w~ = 0 , %

z

1

=

p

j

j

z

2

= 1 z

3

=

p

' "-

2 1 + i =2

2 1 + i =2

"

" w~1 = 0

w~2 = 1 w~3 = 1

. 2.7.3, . + , '-

" " - . -

" / ,-

,

' %. % . z z1 z2 z3 2.7.1 :

z

1

z z3

w~

1 w~

z

1

2z1

:

=

:

1

,

= 1 w~ ,

z1

1

z1 z3

0

1

0

1

z1

1

z + z1