kompleksna analiza vj. 01 - 08

37
o=h+Vrx1 * -f,- =-T"r z 'o - 2m\ T.2*l 'rr nqa Bp n l| Horocau{ r * = r?, -"* '" au [ -R," ld +-)0 - P,r, *r, : z (: "z ,?, - %r1f +.><, =r(L}*)u) =zx (- I t *x=Z 2hnl { ,p ."p>E n nb, * 'q .lJmoyr anp. $,.1"e.rrc (z o*nz. B=\,-1 e 7-.i- 4 'z.lz o Z: z e>Ul )/ o uz-+tz = t=*te o A b[q 'h.?rro.o.l,]man 'n\s\r^"b (r i T:T 'r =,! _r-;(:-) ;(i#h)=_[++"+) = *ffi== tt -!-=?ml (g=zo6 1_ = t) Vur-X = 7 ?rr-* == z -> d W I ? i e--'-- -- _ tnnt.Fl * 6*sz,.l. t+bt.y) + X*sz'UJ raoa.tn.r4 'd*'-f 'I 'r - 'tl ts.' 9ol , - _ =z 1+ y !:' go}' orrP Ynl : "t .uYrroJpo t" (z furo,t- ;[*ix, '[t]*, t[r1*or n= z-g,[1q.[Yr z9;61;*[ -[tiS " m*if = rt (l.,t**nQ-,x\r + zfurt, -oy,\x =(hn3*)1r[,1+ru; = -z .\Z (hlf,r1 J + (vx,Trrs) = "z+t* ! - =e.*rp ) T- =y*1vI ? = l-ia\) '[ = xr] '[,r *10 =tz rCri ttr = \u 'q fl*-1s ,)pw$c, aTu^,lo,1 - ^ro.&t^q r&m-a xc"rw.rr{, -^ 2og = 11, ?r1*r =6 Y*ati=lZlU J r+m\ -_ Iz ml '|,h'vx 1+W4 'Orno\ YDtrud')Irr <-? tz = lz \Nxesq \Nsl\luHcnn

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Kompleksna analiza vj. 01 - 082014.-2015.Odjel za matematiku

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Page 1: Kompleksna analiza vj. 01 - 08

o=h+Vrx1 * -f,-

=-T"r

z

'o - 2m\T.2*l

'rr nqa Bp n l| Horocau{ r

* = r?, -"* '" au

[ -R," ld +-)0 - P,r, *r, : z (:"z

,?, - %r1f +.><, =r(L}*)u) =zx (- I t *x=Z

2hnl

{ ,p ."p>E n nb, * 'q .lJmoyr anp. $,.1"e.rrc (z

o*nz. B=\,-1 e

7-.i-4 'z.lz o

Z: z e>Ul )/ o uz-+tz = t=*te o

A b[q 'h.?rro.o.l,]man 'n\s\r^"b (r i

T:T 'r =,! _r-;(:-) ;(i#h)=_[++"+) = *ffi== tt

-!-=?ml (g=zo6 1_ =

t)Vur-X = 7

?rr-* ==

z ->d

W

I?

ie--'-- --

_ tnnt.Fl * 6*sz,.l.

t+bt.y) + X*sz'UJ

raoa.tn.r4 'd*'-f 'I

'r - 'tlts.' 9ol ,

- _ =z1+ y!:' go}'

orrP Ynl : "t .uYrroJpo

t"

(z

furo,t- ;[*ix, '[t]*, t[r1*or n=z-g,[1q.[Yr z9;61;*[ -[tiS " m*if = rt

(l.,t**nQ-,x\r + zfurt, -oy,\x =(hn3*)1r[,1+ru; = -z .\Z

(hlf,r1 J + (vx,Trrs) = "z+t*

! - =e.*rp )T- =y*1vI? = l-ia\)'[ = xr]'[,r *10 =tz

rCri ttr = \u 'q fl*-1s ,)pw$c, aTu^,lo,1 -

^ro.&t^q r&m-a xc"rw.rr{, -^

2og = 11,

?r1*r =6Y*ati=lZlU J

r+m\ -_ Iz ml

'|,h'vx

1+W4 'Orno\ YDtrud')Irr<-? tz

= lz

\Nxesq \Nsl\luHcnn

Page 2: Kompleksna analiza vj. 01 - 08

o

E\

t*o ' t =]'

:\ E-\ n= q f=Iut=\z\ r+g! =z (a

t-<t'olr^ '"' 1l

}"}0

6

tLE

qq- =l 1:lL '\ \ -E]

T

sl

(o.gl+oqao),4== I

( t-s '' n [to7V = z (:

'lr=\

o=A

A =lal

0rT =A

-6=tzi e

rI-=z (F

.U i)

O = I..v1

0=a 0

It =? (t

Y_.--l1Lg -il

(#**] *,:Etoa)r -z (-

*=rhJ6-.2

+wx"d1 rDlrlclo'$\,t .' r.r'$-crr1

he,p -) = (A,nS) t Aqcrt ) t : z : p<'e1q'dhc?(zv1t3d' xonobt\L

b*rru.,r,^J\ + p'*$13'yryCInle.fir * "rt',"d\ ".p

Yml <F \ct7vf, -+ fr B*,, =

^

=rh

a\ri'.\ *rn^' 'Lar n- =Lou = zB.rY

= o\ t/d)

zau I

iI

zrnlJ,

' \ccgg bccrsasraHcfi 'zl]\ad' bt-.al (+)

Y"

T'= J.',n]&

+Y

+T

. (rrr'o] r.nrnFe{n\ w -0 f,ffi^r\?t+-{,, *0aV = J. -e--

t

.,t' I v \a\ Ili"^-'t r r , -t p-..,t, -'( )

)i**1 (r.-a\^n 1"<,$r1(>rnrcrvr,) Tn?cFrr( - g< ,?, -t_l = { = lzl _\r--t-Y)- - ,Zl? -r!"{ g.rarn'r'\b - r;,

T = "[)-,o)=tzr

(r

(ez

Page 3: Kompleksna analiza vj. 01 - 08

@

.s\c\r6 \, __..*, vg -

'lr-\\r e.,,It V? = # Vll 'ef

ft*t n i-n* = {( T= [?l

,Z

l - D =*

,(r -g) t,'oeJu{ ( v\

oztz

= t] '\z

(";*ll] +ttrtm) a-) =-2

(tJ.,.^ts r + \Jrcoc'1 5 = lz

-,\ s Sn-,ffi-

F-,$r"0)0, s = * U* f\rtu * = I,

L*)A=z

-:l-g^

*a ?1L)l

e _ U=lg,il- I- '

r-vu' ''o=r '. t;fi;vs \ + #ri **) dl, =j-F'T/rhoro\W\-rqf rr*d \ncr\tn '-" 'N\ a lu' (a'w)ws I + (a,w)tor) r"! = uz (I''11,t + gooo)s = 2

S\nlflal Sno3an\oh

(t* -.,r) *w ! + (tI t))t*) +(tox*'4rx I v11\voo) "l '5

(n{ +r}r=\ yn) }l, : Ih : \ =}y c= 6 z : \7

)+,\z\ r'u ns

Y'lir = * -"t-o -- h

1-rl=z GLz\'

\^= _r_

= IvL! ] *'[ Erol.vJ * T :

Page 4: Kompleksna analiza vj. 01 - 08

f v=a "z

I ,=r.,,Y

I o+"r8\T=At:

Ozrz,q: #'rrtlb=z cirfl/

o.rrri"Ynrrn

C\U

,]]')6 t

(aetqvpnl^aYntrronz\ E=il

1rlttr+ fr = It

lrld+*=l*

a!

"l <-+=Atw15

3',)b = Itt{}\.9 =(.2)*t

(ar*"rt)+ )."t to)r6 =zz (--- (ltrgt+drto^o\x =z\ti={ c l\pj=zb=(Flq'tr=\?l

A -71

T=7

o=7

(z

?= [I) \Jp

?= lLI tun

J*4, vF

:"Crl = !z

=!Cn =?z

=\-'z

'Ycrco=a

T =tnll # = h

L

*6;E ult J'

$* uit .l=,$e

= [Y)

)- -

)-=Cn

't) -:t -\

)- V 1-r rr!-,---€.

I-I )-t z'ht)-u r'

o: (1-t) -"?(ttv) J O:? "1,

o= (ti -r) -rz(1+r)z

O:z(i-l)-u?(lnt) (,

: aphru ,-D*-Doncrrr:r6 1!r* a ?.b rIX\r (z=

ti)(.N*, un $. ='P

Br *, -Ij= '=brwr,,Id =?

=3,

-6 -a

T=)

C=I

(fi *ro ) ,l =*

'C=lzl ' jrI_

b\L

(=z (q

\tlto=tr

JIIJ'

Page 5: Kompleksna analiza vj. 01 - 08

o

'e r'"''l'o=1 ' #*t vo &i:, = aZ

* {=\ (:'\p,-6+ft =i.TLu = ^ #J:\ Ae t,F aJ

.$r=+(ir)-r e 3= s{r (: s{,= Dr j t(&- a-)t'n E-}r =

ku, I . (a)sp-r = (l-rJ z = rz

*0, u- nn e $ =i Jr=l$l i-I -on

(lt\F t -- (ttw.st+(J.)to,?)j = (trw$)-J.cm)r = ?

,r...cf(o--it t,fr

4S 31J 9-! = x?

AvPJ = a

(i-Y)2=?Z (o

(#*H)t;o'7=az

Gk.-?)\yg 6=rx

'Itr,to=7 (

Page 6: Kompleksna analiza vj. 01 - 08

d'n +-EV,zl 7V,=y"F(:r="**"uzrf zl - -=Lo * zYz-

Io:rV, - u -\ *rG- ,t* \-AI

,wv o r(t-x) I = Dl* rB -zx,

;-,u[*r(,--)] -Jg_du =l[-(v_lql...\t^+(i+Ql

t]*x==

=\!-z\+\i,+zl

D.W\< x=Z t =l?*r,-zl il

(,Iiu

I3/

l,' 3

v=

!:rtr*[;+,(r-r)

s!'-t)il l(l * 1,,11 +1[ - r') (:

'Sl/t olq1

'r'uA !x

iui,"):1

jv

oh =uh*r* ,: "/

u = .=.[*,! =,=, \*1** =7 ] = l:t (,

, +a[r, t&r*$rntrp2u ttt% 0 = z -1ln) &q* yr'r"* .d**,1 r +Errorr* $z

Page 7: Kompleksna analiza vj. 01 - 08

@

(L'u1^ t .on );a =

' )1J1, "'oP"yd V

^alv:rpoUad * * ''l =@uEv*EG)t =\\\\,\\

VCrlUCnt ,r',U atfru d

?r*,qrel

k*E

Fr* h,n) 1 * ['r,o * ?j nn) ""

?)1LZ

= )(t rr +?r; *xa :

1,61i+Zd = 3d

*=,n T=rrrn

o)n,z? = ';? 't3?

,?=', ,!,uaa[*d, J

:'oN='Unb

e "[ls z

ol*a

-t

otr

"1,

"a

el,+,.t p

)cp nl

Po adYCR)\crr+ \NnVCn$r\aJS)t3

ffi

m yxl -____)

fh?lt ----rl'z

Dn},hrtr + ,W

+"h

Lue = (l.*r)ru

L -o = 6?,,tr'1ru'

=.qLl+, ) =rz .:2=C{\z

1, (:J

lrr'tt y- - Z

'rh,r

(z)i' CI

,2 =f\ h

l aU ,WaWo 'U

(t'")o) t(h'L)rI, = (hr-x;tr- (r)*

q" Ynl -- (hr) S = {u

e?p '%t *- (r'r) tu = il, w h

T1+rr, = ft=(e)* :*---(r+l

a1,6o\1lrn d^^* ".lJ

(---*_ ---'?'

l\J .-lF,J t*l J s U

I

I

t---I

i.Ir/r*rt-

r

t0 o,r*t

3'ltYc\u\\' uAcc)l :co'ANn+

Page 8: Kompleksna analiza vj. 01 - 08

I\qh"*-l,.oo) *s

=p

t

[ ., h*p, nvv-:tt,

"h.YF + tuQS) G t**nt- l',wo S**ut ?"t'co)*a= A l&'![T:fr[m* -l- - -----l--t.-.-..._--

?-wtrj - hsoo

i,kq8-3 -?,,tnoo3 = (\h-tvr$)+i?r-)too ),.-e = z

, \ )x\'o("q""rrpd$rl -T; ?3

aI

_a

l??a

t?

>r".vf,"u .--rtrvJ

n ln-h*f " = ((hw$) . (L-F )." = {,,-*e =

(L"tlr)n -(l.,*.1*e = (flrs,t* hoo.r) ^a

3

a:

"a

F

4: [r1.*=7 (

(, G=

ffil \p.fu *,*,9 crnay,m f ",hu,olg ?[

o,rlanoncrrr{Inl..lop "\,l &,o } * o *- ftt'}i -) * T ,J,nr.l.q --+ 0I

r

(r.}v)

**L.'rr+xi) x !ll.)Crnr alnu *a

o

o

(k*r1"sr* (?r,xz)too

?r*, *,o.

?r*rorz

= ,tDrtn

*)a (:

: \rqLqhodYcl

,-I?=ffi (.,n'+c,

tr- x? " fYl hnl

zz

L-f = mad

lr1* * =, h

3 =c{l ('-6

),*r.' = r[,xa *"Pr-"r?

Page 9: Kompleksna analiza vj. 01 - 08

e

/_ a n'z: vur+x, -hy+(*")nT= *aUr,, 1+ l.al-6 - (ra)\^I

z= (f)\^)- (,

(o:z a6 o.vvrrB ,lehn)1t1L7.6'+ Z

o*4' = J -

l.rY+ x

* Ita

(-, * !, )r * (F)ua- -= ((Pt9,V) r - 1,, lu?- = (.a)t'r

z ; (ra) r,r (r

:F,*

[r, n ]L'lr-,tr + 1L -) x^61 -; 0 uf

(r"r, -(*tBru)l

lr'1-) *U **o'vX ' ((*)B,o)t+)rnl)rtr = mwl

,\ urO*o5rn rrunsm,ri r*XLc.*[.rop e o:1

,lfr*rq tratryn"q PoSq >r"olt'q'-?

Lit'rr) .-*0 r Utb

C\

l\{ ,,n*d I c.ryren,rqsp )h )to!'4$ "r

* Icr lT = (*)%y I + lrn1v,tr = (r\) "l (= z = (m) u1

11 I n'=3t-rrB+*LrU = mBrV

*] *l :(hYlsi+ttcD)F = 3 h]*:e = 7

(p =p * Sl * i aft\ ?ow c"n.qa] 1Y\ .rttrlg ,z ) F = =3

Page 10: Kompleksna analiza vj. 01 - 08

-b,*lt ^ ^b,'*mi.b '$ O=ri el tlu .mnlun \G.quwaL

Jr,/o\:(rrqtr* .aVlu) l\ ta6-il- t'

I rr,r - +- = [O, "i)] rIt-L rdtr ffi+ "rtltr- +- =.ffi1v : (.,,*-13)ur:(lz)u1,e = (.olz1u1 ; rpahrn tw

= (ll*l rt,

(,))'l Jtu

$y,ropdo ']6

at,,F!

?arrlr- t- 55,'

It,

= r(rn6* t) P =

(b

',1'

1,h

l/

_+ a H-6 = (U tr +

/ *t / .'/\ -i.a /

1rrr,-o . lo)t = Fn,

. i ) I * (r) Yrd = par *

I\zrT + | : Flt+cr)) a[lu) r * lel"r = F)u1 (i

(:1Lru )y *

o=I

lyt-6: (r,)t,r

: "lnca.)po

(u

(=t

(q ,lr* gd9 .,,.trf : ru

(4r"^*d tTjo; ,\-?nvd - vt

paa-o

Q a lte c

(..--.-z

7 +--_- ZV

Y f-I \ rn\cncrcrndsX? Vpo r rrcnterof -,/Pao (s

'- *l?z*.[ *

: Yl\s,hrh

Page 11: Kompleksna analiza vj. 01 - 08
Page 12: Kompleksna analiza vj. 01 - 08
Page 13: Kompleksna analiza vj. 01 - 08
Page 14: Kompleksna analiza vj. 01 - 08
Page 15: Kompleksna analiza vj. 01 - 08
Page 16: Kompleksna analiza vj. 01 - 08

lLrrt +

(w'lb

),*

acs.\ i zT=*\3**P

(.::\nt')'r) l-=r$

)

Y

t?.U

a\:\

+)

n

+ (o-a) .l)

\1.\' :z\*.[

\- =

\ ]-=I

'sd

-*_!\+? a(\i (:

'. zt-l\{ z = J-I:,+zv'jErritocn\" = 1

o- \ -*\e ,T S," (= T -.cnia = *lt *A

t

*t'/ .,3 -*,a = 77

3\'r(-

L-'cn.rt

I r,+ o: '[ - 4ZZ - _ 1z

af *,9 -*F = OA\A\5 - Z

E;o-',E!fr*' .a#= =Ii': g:, r

(b4, ?l u-l .r - - \r-i (frdoz)ul -o.rl .. o= *P/\

+'Urd -r1 (= *,t -X

c-'[ tcnr?ffi ;,J-..??-6 = l**oa$r

1,

T=^l-a = fn tffJ = ?C1\\ - l'tt\

a\O2?JY - $t\

v1 Y(-vtba

' *\j- ^t

(*lJ + 4) \,'-l )- = z YP arY

_acd'UIShCT nt?

Page 17: Kompleksna analiza vj. 01 - 08

Q)

0"? fuxg P..O /f50-' q

hu xa,

@"= ru

b = ft,*sF l+ Kcoop =,(J) 0 rl,,u -rlgU.tfoto d "\} e

D

ht,o0*n =k %**-, =ffi

ff,*wp-= k V.rm3 = ffi , :rJ.rn,.t-r.\nor[

(f'pt off,ooo)r.

' yn/t"rvcrhJ .f clt.q l**h vw ^crh3.ey o)1"0

l',*g*a = 1?l"\x;5t,

Btoora = 1L(x,;n

=-a e Rrr*r.= = bE

z? { ep +ll"n.d (=

U dOtup"d Il, "e$ va3,Ur;erm Tn'nnrr --} x "o'pno ' U "ol3rupd .rr1g1 Ln.r1rns rD 'cfonuap t

t-z alrgrr- rp.Dr, \.cnraw ru tvro sspn\Jep { *ro z

({..'"x) H - ('f.,"'v';

1;1orc?

fA."r)+ = (d.,,r ffiW W C\,!fg cryTrcS I a",f6

:{'ov (zY1. \"nl(*,rfo\ryD

jrrrgrq lo-ro: r,)

+ (a)J.rfv ol* '!3c

-O=IJr,t d rr-+tCru' '"*) fr,.({'"x# = Cu),t a! 'zpqb ' ?)> oz rv 'qony"p a

,.nlmr1.1 apahrq q'q"t,'x) l^,aart. n, r\\rDl".^^qrp

v

1,, Y

U)(d,*9=? rnlpr n'sv^\ail- $ Q+-U=?;r;qfitx,'lrur+qPr,cu'yrrr=(z* "rhvr,rr,l

t-? 'l.,tr

C'?.,,'"*) n,aw'pnruchut ^\ W ytr\oD(p e? &t*ox., = }lrvrerrpfrfe.rdaW ?t +

'( -R '?. *-h^

oXr-x ^ .xc-x oZ c-Zd,ttc)1,

-;Y^fl +(9r'*''yn, ;r0"'= (2>t rn.rtr ,D*!yq

f9-'.*) )r \ravnf ,%*f -0u ) r, cryno <+ 4r,, *? =of n3q ru \ramnr ^?mJ t vp stnlu+

(h'x)&Y* (?,".x;ru = ({Lr+x;j

5rc61qo(u('F'ctt Vl

9'.e

ne,

vf-* L\Qctgltr-rvNv I I\aN'lrqNc,ror{3y3-jtQ.

Page 18: Kompleksna analiza vj. 01 - 08

B

tl^:u)1i,yrD .\yw e .,n[* ta .,rwu\v., qo* .: ] .rO, =1;l:

&{r!r-=

x='l)-=

0=

I'4,il,

?,a,

m'

c'=tr,

. x0f = ne ?rr-r =

= [?l =fit (.

(['*).r,

(!.'r1n

?=h (e

'Sr.t" td np.hn u,r Pt -,*un'nm JvY (:

7z =(z'z;--l- ^= IET: ,=.

(uB, -r,lixT ;)c) - ,(? ) -

,-$*rx)[*r- = x-c.r-t,[+"x')h - = t(r[**1hf,tr - = ?rf (r[,*"*)o - = Ht- 3-

,($n,x) ,().t)*--lmr-r$'= l5

,("0*r*)I + -----1s-,, ,\_,W-ctrS,qnfornO

.(rt+rx';,1rR+rx1

,x, ;r

rrn

"I#

!q08

=

0

tid

,\rqr--Ei -

"Y -r%

$*,**-r-

ohor* ,h-.*-T = S-x-

= -([1)Vv+ (r[ t,x) l-n

-

,(rh +rr-) xa,

-1.x4x-gry = rQ

"R+rx

[ux

4[,11o

!tt- L-=-Vrt_ K

= 1['r1 n,

= +=$

xU=G

x!,= r-0

t"ot-r--nB

o=$

fi,. d','*)r,

x, = q%'t1n

:

7(%y* p) = r? = rrt ('g

1 . 0!+'[ =,$

frt* * = 2 =Ctr (b

ry\r-i'o -*rit eLl5qrrr'iwrr

t m gornlsvrrorro .thrt*r (E

Page 19: Kompleksna analiza vj. 01 - 08

I9e

(:

(:

@r ',fr[)ff'dli.,,ll_r-\i; n x,

?o=@,

xa,=hE

,,?, -?r;t, = (h'*){t,

B*? = (rqr$ * ?, *U

o=CuB

(*)'t*oh..&,xt =61

'btu.nrovrn $pn=# 'p'\ {v e e

= 1R,x-1it, (: '-l I

x0 t$--:

...-Jrg n$

xg=nE

(\) E

Sq,-t*q^wc2,

(rm).r.ttlrrv ua cdl g oTn1pllpo

x?- ='h

*v = .\Pg

i'o,,rt\t*c.r.np( { w (-

O- Xg - XB = l^uV

G'^tnf-,ttr,r1w {21} .,h nU0 lry \1rTa.t\wnrrdu

( *' urL.u.rrqrru d

. --r--

-

(jmabn aut {oJqD) ;rl:crctahbY+l (t l vt, \[ rrs

y66rt-lcdvft

flxs -

,k -"**

B*s = (0)U n,h - [,,xt )

t@k"?,t

-;? =H k'\rnlsl]"tr0w0 I\U rll . t 'p'1

,B'xc -r"'' * wufrj,m$Yr lo\ yv .l { rymrnlnol(

'T?rg,$rrprro ,But 1x, = r'] oTp rU d, \qbrh ' l!* fr = ] "U

'p.] (V ]rl,parpO (sz

{' f 'p'h '-d**lu,r P;'#u$'ff,E- \cpTll. f{ rn6tyncrrn)'9r[- Otrglm o?fp 'c(t

vqt* r-U-? r+nqlw &,* ., 1

(Cu t ru) arUlpmnnl"Y *Cfrp alaru rx ok /

'0=&V Y 0=lr,Y \t

bpal trro.u.rtont {r,!+n=J vl1 { r,v

fiq =YQ ,o=t;.ffi=Lv S

,p pnl1,,r, r (g)p avrfl4 rcrrn S ctro ),. b 1PgrunL v .t\yn*"lovd. + ([,rl;, ,[+ '{3q-

E r+tut : \^*t=x*Yrt..L'PKtstr = rh

hmop,l = k

hL

S0 tr^ d,Yrytq\'rxaHrwt\!4rr€fi rlr sp

d, { rO pwnu rvu '

hnw*nx- = fu/

'lrr,aux : k D Xg,wrnxrm = i(r],)h$X\.oal+h"pxw\ =

hnpxum = (h'*)ru,

L*^r.ru = 1R'*1 ru

?w.\B = N (f

?rr!\ q: +q'2YqitJ

iq3\-"P'm

Page 20: Kompleksna analiza vj. 01 - 08

G'

YE ='0

b /b\* lJ

o-? 1*

- i-ffxr')F

(t*-,8-,r'1 . (z)t

f ql: S--.Q$trtctmS-

rr + (*L

s- " (l{-i)l

- i.i* )r *1flxn,B*) = (a){ e

?- + - i *{,xr =ry d I?p onr'rru

ft-==tt'*trr? (*)Q *

-rJ Jx,-=(*),0

r - [t = (*)p -L't

XD. XA,, tg-=tG- rq-=W,

S =?r,*x-6. H

x -k = 1x,+ffrJ

t-?o*d=1t,'*)t, (- hl /

\ O=Y-6 =DV

'un$\,\ibrrD crr 'p1 {vg e oryJ,**r1*6 | f-o.t,1x.rt, h

S- = Qr-t)!

h

(v

Fllt ]+g- s-

'-m|=X.

,.]-=g)u.:'t,

ts='H \o=krvv o

v z&l \\, XA,6 = he; Ao = @

z

tr*rt,=w 0:rw

*,** "\} 'P'I * o**..*

'-)'l+ 2 = "" =\./.'E

0'*)r*p (hrxtn - t?)t

* ilqo t ?-,**I-*=* c'r{ru+ $ro I\t orr,-(z)*'l{v D***}'yo'r@ctt (e

'01+n=t

lu + 1Ba'1v$81) *,qr * = $'x1cv S \ql,,( (+

c?ru ' {i -r,qwrm a}-,'q},u (sl

P)ru\,{'ffffi;:#.: oF v- d+6=

^o4.l,e"Tpr^m apnt ( rD*rx', . (h'*)ru )

Page 21: Kompleksna analiza vj. 01 - 08

I

;ra[^^^1r6 (n)] ?p ] "[n ,r'^rrn\rnrrtvrh,n* "orncr

I+ *k -..-Q." O= fO ?> O - (rn)V

"(ffi) T = [])Y

-

0-z-Y1Qt

(,n)zU

(ez

'knr.-,lk).--,rynr+

*-*rv

t,F*.,ffiJ " .- [lk) *,t*1 . =

Itk.'H,,*Jk) -,lH)].:

?'e ?..4, *-'t W' RU o

-t ?r?, t hq-\tr181 0

'&nf=: (k ")k

,(0 y\r , x0 xQ, *fl-.g'rt,+ &' ug b

(ffi)?htr+#'ffi:(#"rr)t=(G#)+

-

z(Q cr= qpp (Y..'t)Yt, = Tiz

,?Q .xe/r-

-

Lv (Jo).a'(,h)re

u 0 =lv ,q ."l,

n

/''o "ffi *z"

1

;ni)r"o"rrtut1 znr I "(7

zXQ'

w ) o-nv: OnrmCYtrd

,\ ,,"^,r\' ?t rrl (tr

Page 22: Kompleksna analiza vj. 01 - 08

0

6o

^dl = Icto ' p+ yi,.? = (** (: o:(o)r,*

';ltHt -iffil

1"",i e

' +1/naTt - Yye

A_

zxQtrg

l)zhO- Jzv

";*.

1*

"XQ..--:J"g

xg]E

t'B - "ffi]*,,* * Likl .l*l r",,,*

.B

ffi 4,),& .=(*)(vu),,* = + (n)r r

+(,,),*- +i*,,-e

1$?,.(t?.cr;rr,)1 = (r.lf

(*),h *"(B)a',,,t: =

+ *n E(rF:: (+r,,r,*)t: (fr)? =

*ffi (Y,)rt:

o=.f g u og)o( j'Q

,Be .xo.

1?,.t*7"i, =r1, ' o= I,g - 'f

.rnlvy ru t O= Dv

"6 'o1"ly"t".*rr1 ru dvrrau (x

5lo"f / bo/ G'9,'0N 'vx

;urslmo,rn\€1tr \a6otlal- (t l* + i gl*

Page 23: Kompleksna analiza vj. 01 - 08

o

-.ro =l-)fpoj lruA ry + .-"1,.1*rL \, -.1,z

, (9 = "{v

-LrD'

,r-r, _r(J) = ,O

(nzo)(a)2+n) = (*-j;t(,b+n)E =

.((.r*-) i-*){;,"*)+) p =,$

=ftz'

(ur+ t) * ="e e .b1*E = z%-r.,!--r)L = r!

Vw1twDt_Crr

&""x = (L'*)s,- s i. n -

=W 1b = (lvr x) \rt

4"0 r=D=v ==i?,t + x)= cg

,:tlro.ar \-r)-

.plr afirNd 6 +L " (z

rB+x- =

Yt

2=(I\z

J="[+?Jv+fv=fi\

rV aw,rrvfrDJ-" El rO - *i -r* = m -"!yr"r"*3 [v]-rvoro)-m

Ll'ol ) I\

(**'0> a r,

'"D'tr^nw ?t$ $rolpyfi-{'I w aG )"r\}"rv}![

LE"-"oJ

e. (*'* -)

""y'QLrrj $*t

{r*5**n = iu

tlo*3 = n'

!$z+fl - Cn

ar-*

?K

[ ]ro*t$tt -+ 6rrBlu = [h^,WffY\!-(t, hJ

I tt"ncrrn --r ,?: h

GxI

-? =N

=a = S ',r,")rcr^n1

^carr&od il/ YvlFrucrD$-m tu ollvurrod {or rr,

vN rct^Yd |treeq3tao ;RcwnY),{\135da

ib

/v./.:< SN\a'--\-

...il)'\,/v-'-'h

:h,Y" = =

V",ftlrrold J *

AwfYvcftt -= ,- f,, >o "rS*L

Page 24: Kompleksna analiza vj. 01 - 08

o

c.Y+f. -={}YUV

G

YU ZN

G\\

i (**'f] >$e- B +z)ou[ = {t,' "'''

,,,

\.o'* -)uw,(: tX6 - = n,\./(ort- -> > l-t (* t* ^) 9 X

-6+ru!-=.tv

a 16 +rz.g = qn *\ rncal,q,.nrenro

16 +zzQ : cn = (z)l

*.,*-* ro-n l-n,rrq)-Zn\

<r_-(oa coo-)3

X

t-----___-/YG +zz9. = (a)!

iwFtuoa}-.z 6r >ci= Q- "Erralt-

^cattard :N qD rP

- f --- -- a---wl"6nnu1 *-*1t 45tald o

Ywl'YvrYlcJ-2

ft - (2)+

* -.0 lwrrvmrr3-= o, qrlrrl^yX) algvup,ol- ^rap^^O w

tGa * yofwo'r1;-cn n 6$"nr*; al3vilno{ ct',.'l5wb 'r- (?)} oQ o-',-.,cpr6 aP :-rr<r

$^rt .G f ynl?ne^ d- a*u+rq tryyrr crno (xl t$-ara.ro.ld o^nynJci\sb 3,\ ."^fc\rlT

(u"*-lyro&v I u vw \cr1i,l-l-yno',rD - t) oNL$rs\vA1Nn A nGa o *1r,1 J'roc'rxniaJt

sc$vnY,1 trg:ruJ C,nY'1jc.t}Nc?t

i |, : f,,r '"toqvrJ6 vnpmst .,6, +ra = 6 oQ rnr'.1.rlr* q: rv +(

Page 25: Kompleksna analiza vj. 01 - 08

0ro=)\ t: 0:lb' Lf 0>? H r l

rno -- on\?Jb

It"

(O'rr1 1: ;a =H (='

o = ?r =tBlU

[]'a) . *"= H

Yl,\i:-ii--_

(r^l[ -w

<oo -to] > y

t,\ io(rti'"f "

(- R= crBru,

T:o?:-A=H<:-

Ll"olr?r'o=x 'ql*

9p rffpnnr\

[ -od

/?roltrl;3 \ o=Dep-H i[o'*-)>x

>l1n\ I alg^,rnd t^Ir-r ^d,

^ l-(t s* \\s.or)p'= -t tn p =;a . m

<,.,*.(] >.0

-Q:t\Z

"xT =.\, (: 16 +xX -zxt = x'6 + 0 -X) YT = {0

tr =w *(;')-f- (-/>o:{-\=n'

'1. il\'\\ "

!-r(o" tol

<".,v1

=D

,D

:X

'-:.1- - _r.- ----\ n

\ ->

x-6 + hxf = .ltr = rn Ynl

\ - |,rl,--f,, -,* = T, = cn"B

ZQ/-D.Df.(*tr * h"I ) l+ rv$ 1vil "rt,

: ttr

Onrrttr - xt{ + }hx6+ r,W "* :[Y\

(otl).v .r'

t,-X

\r,**=Z' Z.t6+;=t'11

)icrl ho/o\

t'0N vx

Y,,

TTIuJI, Vrtr.rnard :\ ct! n, z16+12 =M *"U v-net3lfl^rornlt"r$ (

Page 26: Kompleksna analiza vj. 01 - 08

[''9J" +0= l{=Yr'

Io'll ? ? [?iYrtr=Yy

* z9:o = 19

\- o*l' = l+\w(t = w

o: zBru =t-Ll'ol, lzl-0" = ru

[o,i] = z9luT=l2l "'P

$ - zB:'o

Lr,'';J ) rzl "'o

tt"l = ,L,o, Q-\zt .-.q

5: *9'oF a-

[a i,] a [?l

o=h[alvl s x" "'4()

r'

\a:l

\*I\l=n-lL

iEI

z9tp = {v

l?lwf = 1, eBrtr + lzlh( = irt

O=rh (: O :'l1-}T}r

c>: (t1y + yLrv) l +l i,lnf <:

6lr * pBru) I + )z{ n"f =

<._.--_

0 =(\)cn

Z\rf = ffl

t

.,0

;-E,

'o=(qcq a'6o.r-7 'p'I F"Ylt -drYlad a{Jyvft\".! z d'o.o*tr Wn."f,*t ?\r-1 =cl\ ".".0 (z

Page 27: Kompleksna analiza vj. 01 - 08

fu]* on.s{ lnrlsorrd, )?l o,mrrEr\p..\trq, -rro..*r[b4 =tr[\ =nt

t - q+1b = [I\

xt=A? { r,,,m - 1:=, ns

=*

o., --'m { *rr' 1** - * \rl$o \ crn)tu1, .r\ )rl+ b4 >rU\ .,rrrw d orro o

?n{o r.,.}nlod*l h=cb sZ-zz .'z-z ,c,,JN . ,ry,,:llt. z 'cnJt11 . 'ry,,:m m=(iztS

.z: Ttn_t1x. ' rm-Cy\ I l-fnrnlcl od omrowrnoj 'tH 'rpr4 v6= (l)S a cnm olz _rz lz_

algq 0 w Uvo"rpnhrn arrln\,r\) ?$rvrb,c) * *n, bnapaipo cvn2{mr,rrp-$ I *n**\ y\o\rny4oN

.[nm.,+ ']b\.vtp zFn\t .]to+

(r)s " G)s "(t)s " (v)t =l\\,c

3f "d*h r+= S.*=*b uno !o \I\rd n"\pyrrd*"r\ {, ,nlo}voq )^c$/ni\how nt/rn^! v

(F

G

(r

(l.-.l-\>>r.)-/-t

,'D .g ,n \yrv ) ,D*oo = \ p-_ )g 1 YPrlwV .:-

laqs;- vrra4 cn've'artatrv^{- .zyirlocrp &

d"t

Kf-_--. r0 ^v1 ro\lnryn-1, str + z = (z)s

, r..rD.""rya "t6.o\-o'Je

: g t]} c"*Fnz*pWl nU

whr,$ [."tr 0 = 0 c

0

0

t thr'hg^od'' cry\y\rcg\r'oh etr.o.*)u,{a*d

( )vno? (?)s * Qbul)

o+o$ -^{oU }3 P'?\'u wvrvna3r.{

-F + zl

"rt - t'v =,S tpn\i,n

p+ t1. I. -+ = (z)9 =tW .u7nqo {,

$ + rv: \"i

{rro.,rranr'xd s{wr^yr ra$vncrreut

Scli>el^? q-\vv\ro L 3 r\cBn Ro H

Page 28: Kompleksna analiza vj. 01 - 08

l-\C--

! *\

(: "'. F

!t\

v.a

v

)-lI

. (*r\-r. ....-Tr- 1-

Y - 1 -t{l)-\-z = l,ltrt t-

o- z-

(t-,r)-z H Ia -----4 =

-

oY-z ')

)+t 1*\l +1, t

l

\ - lv r .(o-R)+,(t-v'))= l,-*t., zt I

\ A*-.\\ t=,2/t\ \ (--q_+lrrr\ t \\.. ,.t\'..,\. . r.\'\N;./ \.. N

\ \ (I"ti)="2

c Cr l. ' c\ ,

dWf \swf'a*trt'o "w1rs\"na^1 w lr > I t-Z I t-,.r4 [r

"x""nnr"*\ ,h, f'U !+I:orvo I

- L---,--- -iir(\ \

\^' \ 'l 0l .+- -

\\[rs

r\ dp ry\^q A ncmtrr)\ ,)nnd ontnC rnl]l rnnl.hu :*1 I Wlfp 3crrn:'S rr

un3{ :^finrn,,iru{ t .VwTfirrt[ d, o^Naonrp (nnnolg) -yv:lq Dvnrnerrf?\rrrp.*o D

""]"r,1fr.{d )Tr\t q.\>ipo crvn}T}I oq{D v\ ' *$ g X * wapapo to:to,lrul uryu$

' tVrforl >< S\t\fillnruywh rwrnlrrrh) mnut \ hywry ud 'arpy*1 rv'1ru-Ih ucmnrn-art 'It1 ,\q

...1.lNI..'qt

.\l_ _r_\ \L_at

\l\, ll' '.. d..-Yf*( ."''..

Page 29: Kompleksna analiza vj. 01 - 08

,, ,;. -

Page 30: Kompleksna analiza vj. 01 - 08

i

Page 31: Kompleksna analiza vj. 01 - 08
Page 32: Kompleksna analiza vj. 01 - 08

ir

I

'i

:i ttr.{

Page 33: Kompleksna analiza vj. 01 - 08
Page 34: Kompleksna analiza vj. 01 - 08
Page 35: Kompleksna analiza vj. 01 - 08

d Ll-+ert)}l- = lqlll

.]J.tLJurt"Uir)+ +PF)JF= ,o(t.4d.(i)*i I

+ {p lU,?v'(n['(+t*)] - 1r)rs . (urq,1ttt*)o1

J= *r,r*i /* \/

1l'*p1i1t'x)n -- (+)| @

1-mr\rn^V ",]*Drnfra *t$^r W)*S,* apdtin) 'VIS@

* u=,. d

N '+T(zE

l*:artaJJ t "p ffi, vp+ 'urr64n'rS*nrt +

*U 'f wJc "rvJ ^r\s).fr(.+W{" f snan$up ,ht^q ^alg.o$ ^omtntB\fpdU d c.lV e

'(ato*^nr"*,rvd ru1ru, o l^,no .*),-i .$rn^* avm,rpSro]Lo -v3rp i 4 g\ay"rr ^lrnnvx

-Ip glrr.(px)* J==nOX J $'op+ ' [q'o] w "[ cror\rrnp\ 0 *- d,] ^"U d omu @

1 t s'o] e+ t(*rB,+ (+)x : (+72 = z

Y.r* a := IE.Y){o'1.bmc2f nt\

y Sr'rF\nJ c.--rcr\rrnT nMnwy^romqlud, o

I

's1/ bof bt'B 'vI\ 'Tl

(.aRfW) =e1 re1. o"F (q[(qxt =V tyoc] p" ntr*r'.Io .,,lpvrraaY Ltryw dc+'l

($[ --3,lp"ul a1 t1

(+)v:x 1

I.frlYnqq vr, \Xt n rrorld I {'vrreu "

5qslcrraYN "ldhQryi =l}.

-twbg.L\t

2P-.-^n ^,d .vrywrrnr

Page 36: Kompleksna analiza vj. 01 - 08

I

I.-x.,/ ?\.,/i\

.,i

nrrrn h^ny,q1 ynl.rnop "t xp l*l J

prl*uv 'g,ou\ (

(rqyn*qJe,v tasl ptc) h^Up'* " ip^1xo.t

,

0 112rpd 'x^J ^c)tEllrforr^o * 4m, ?9 fot:arn\ 'S{

., l-

tr-;l i-=rPrfu= rptltjft,

00:

J%"-' ;\i : l'P' oJ * *P*J =

,}rt,

(^l3P), I :)'

v6V

I.x, l=J

e&

Lo

0

'v

,(o+P

\

:l,\lt

?

)c.r-

J=

)c:\t+=

A

kv

r.J0

U

o(

Jo

vtrC

[\

AY

-.rp

(*",o1 n,l

V ,(tL -6

lr?'! =lL'

6lr*rB*rrldl) xnhw'Y

J*P *oul

lrDUn'I

?*li'l " t'0 "h",t)

Y*L*qn hPl, Yl?,rFf y ti.lSccrrpl S,h &,1 vnlgW

lvJ

J d .'nru r,P za[ | 'U"t"iJ

lY

*p- J

- (gp ?+ xp)

lwF

{*.[,.I'

'l+l'd . ,r&+rxl= ltl

0,,yr Tp=hi-xP=1)r.J

4rnx-,x ( "Pt*l I

o lwrul pt, t rfrr*rDannl rqnd, o IB)^0 )vl

l'l*f

tl',1)1(I'[,], Io: t+)8, J *lfur,trnrwnralru

frpr* xp=*p

tr,u*=U

[l'01:[O=x? (- l =Y

o:h *- o:[Lu'ol a x

(,

WBiLvSJ- (h* l*xpx)l -,h" !+ xp qf= "p

*)J + tp + "of = *o .*i

"!t J

iffiJvl

Ti, =xP'.}'-b

ft e\

f=fP r- X =h

\,l

t-

Page 37: Kompleksna analiza vj. 01 - 08