ENOI?E*ANEAss NI?AAEA
Eiiieaeniua /enea auee aaaaeaiu a iaoaiaoeeo aeey oiai, /oiau naeaeaoue
aiciiaeiie iia?aoeeth ecaea/aiey eaaae?aoiiai ei?iy ec ethaiai
aeaenoaeoaeueiiai /enea. Yoi, iaeiaei, ia yaeyaony aeinoaoi/iui
iniiaaieai aeey oiai, /oiau aaiaeeoue a iaoaiaoeeo iiaua /enea.
Ieacaeinue, /oi anee i?iecaiaeeoue au/eneaiey ii iau/iui i?aaeeai iaae
au?aaeaieyie, a eioi?uo ano?a/athony eaaae?aoiue ei?aiue ec
io?eoeaoaeueiiai /enea, oi iiaeii i?eeoe e ?acoeueoaoo, oaea ia
niaea?aeauaio eaaae?aoiue ei?aiue ec io?eoeaoaeueiiai /enea. A XVI a.
Ea?aeaii iaoae oi?ioeo aeey ?aoaiey eoae/aneiai o?aaiaiey. Ieacaeinue,
eiaaea eoae/aneia o?aaiaiea eiaao o?e aeaenoaeoaeueiuo ei?iy, a oi?ioea
Ea?aeaii ano?a/aaony eaaae?aoiue ei?aiue ec io?eoeaoaeueiiai /enea.
Iiyoiio eaaae?aoiua ei?ie ec io?eoeaoaeueiuo /enae noaee oiio?aaeyoue a
iaoaiaoeea e iacaaee eo iieiuie /eneaie – oai naiui iie eae au
i?eia?aee i?aai ia iaeaaaeueiia nouanoaiaaiea. Iieiua a?aaeaeaineea
i?aaa iieiui /eneai aeae Aaonn, eioi?ue iacaae eo eiiieaeniuie /eneaie,
aeae aaiiao?e/aneoth eioa?i?aoaoeeth e aeieacae iniiaioth oai?aio
aeaaa?u, ooaa?aeaeathuoth, /oi eaaeaeue iiiai/eai eiaao oioy au iaeei
aeaenoaeoaeueiue ei?aiue.
1.IIIssOEA EIIIEAENIIAI *ENEA
?aoaiea iiiaeo caaea/ iaoaiaoeee, oeceee naiaeeony e ?aoaieth
aeaaa?ae/aneeo o?aaiaiee. Iiyoiio enneaaeiaaiea aeaaa?ae/aneeo o?aaiaiee
yaeyaony iaeiei ec aaaeiaeoeo aii?inia a iaoaiaoeea. No?aieaiea
naeaeaoue o?aaiaiey ?ac?aoeiuie – iaeia ec aeaaiuo i?e/ei ?anoe?aiey
iiiyoey /enea.
Oae aeey ?aoeiinoe o?aaiaiee aeaea X+A=B X+A=B \# “# ##0”
iieiaeeoaeueiuo /enae iaaeinoaoi/ii. Iai?eia?, o?aaiaiea X+5=2 ia
eiaao iieiaeeoaeueiuo ei?iae. Iiyoiio i?eoiaeeony aaiaeeoue
io?eoeaoaeueiua /enea e ioeue.
0). Iaeiaei aeaaa?ae/aneea o?aaiaiey noaiaie auoa ia?aie iiaoo ia
eiaoue ?aoeeiiaeueiuo ei?iae. Iai?eia?, oaeeie yaeythony o?aaiaiey X2=2,
X3=5. Iaiaoiaeeiinoue ?aoaiey oaeeo o?aaiaiee yaeeinue iaeiie ec i?e/ei
aaaaeaiey e??aoeeiiaeueiuo /enae. ?aoeeiiaeueiua e e??aoeeiiaeueiua
/enea ia?acotho iiiaeanoai aeaenoaeoaeueiuo /enae.
Iaeiaei e aeaenoaeoaeueiuo /enae iaaeinoaoi/ii aeey oiai, /oiau ?aoeoue
ethaia aeaaa?ae/aneia o?aaiaiea. Iai?eia?, eaaae?aoiia o?aaiaiea n
aeaenoaeoaeueiuie eiyooeoeeaioaie e io?eoeaoaeueiui aeene?eieiaioii ia
eiaao aeaenoaeoaeueiuo ei?iae. I?inoaeoaa ec ieo – o?aaiaiea X2+1=0.
Iiyoiio i?eoiaeeony ?anoe?youe iiiaeanoai aeaenoaeoaeueiuo /enae,
aeiaaaeyy e iaio iiaua /enea. Yoe iiaua /enea aianoa n aeaenoaeoaeueiuie
/eneaie ia?acotho iiiaeanoai, eioi?ia iacuaatho iiiaeanoaii eiiieaeniuo
/enae.
Auyniei i?aaeaa?eoaeueii, eaeie aeae aeieaeiu eiaoue eiiieaeniua /enea.
Aoaeai n/eoaoue, /oi ia iiiaeanoaa eiiieaeniuo /enae o?aaiaiea X2+1=0
eiaao ei?aiue. Iaicia/ei yoio ei?aiue aoeaie i Oaeei ia?acii, i – yoi
eiiieaeniia /enei, oaeia, /oi i 2= –1.
Eae e aeey aeaenoaeoaeueiuo /enae, ioaeii aaanoe iia?aoeee neiaeaiey e
oiiiaeaiey eiiieaeniuo /enae oae, /oiau noiia e i?iecaaaeaiea eo auee au
eiiieaeniuie /eneaie. Oiaaea, a /anoiinoe, aeey ethauo aeaenoaeoaeueiuo
/enae A e B au?aaeaiea A+B(i iiaeii n/eoaoue caienueth eiiieaeniiai
/enea a iauai aeaea. Iacaaiea «eiiieaeniia» i?ienoiaeeo io neiaa
«ninoaaiia»: ii aeaeo au?aaeaiey A+B(i.
Eiiieaeniuie /eneaie iacuaatho au?aaeaiey aeaea A+B(i, aaea A e B
-aeaenoaeoaeueiua /enea, a i – iaeioi?ue neiaie, oaeie /oi i2= -1, e
iaicia/atho aoeaie Z.
*enei A iacuaaaony aeaenoaeoaeueiie /anoueth eiiieaeniiai /enea A+B(i, a
/enei B – aai iieiie /anoueth. *enei i iacuaaaony iieiie aaeeieoeae.
Iai?eia?, aeaenoaeoaeueiay /anoue eiiieaeniiai /enea 2+3(i ?aaia 2, a
iieiay ?aaia 3.
Aeey no?iaiai ii?aaeaeaiey eiiieaeniiai /enea ioaeii aaanoe aeey yoeo
/enae iiiyoea ?aaainoaa.
Aeaa eiiieaeniuo /enea A+B(i e C+D(i iacuaathony ?aaiuie oiaaea e
oieueei oiaaea, eiaaea A=C e B=D, o.a. eiaaea ?aaiu eo aeaenoaeoaeueiua
e iieiua /anoe.
2.AAIIAO?E*ANEAss EIOA?I?AOAOeEss
EIIIEAENIIAI *ENEA
?enoiie SEQ ?enoiie \* ARABIC 1
Aeaenoaeoaeueiua /enea aaiiao?e/anee ecia?aaeathony oi/eaie /eneiaie
i?yiie. Eiiieaeniia /enei A+B(i iiaeii ?anniao?eaaoue eae ia?o
aeaenoaeoaeueiuo /enae(A;B). Iiyoiio anoanoaaiii eiiieaeniia /enei
ecia?aaeaoue oi/eaie ieineinoe. A i?yiioaieueiie nenoaia eii?aeeiao
eiiieaeniia /enei Z=A + B(i ecia?aaeaaony oi/eie ieineinoe n
eii?aeeiaoaie (A;B), e yoa oi/ea iaicia/aaony oie aea aoeaie Z (?enoiie
1). I/aaeaeii, /oi iieo/aaiia i?e yoii niioaaonoaea yaeyaony acaeiii
iaeiicia/iui. Iii aeaao aiciiaeiinoue eioa?i?aoe?iaaoue eiiieaeniua
/enea eae oi/ee ieineinoe ia eioi?ie aua?aia nenoaia eii?aeeiao. Oaeay
eii?aeeiaoiay ieineinoue iacuaaaony eiiieaeniie ieineinoueth. Inue
aanoeenn iacuaaaony aeaenoaeoaeueiie inueth, o.e. ia iae ?aniieiaeaiu
oi/ee niioaaonoaothuea aeaenoaeoaeueiui /eneai. Inue i?aeeiao iacuaaaony
iieiie inueth – ia iae eaaeao oi/ee, niioaaonoaothuea iieiui
eiiieaeniui /eneai.
?enoiie SEQ ?enoiie \* ARABIC 2
Ia iaiaa aaaeiie e oaeiaiie yaeyaony eioa?i?aoaoeey eiiieaeniiai /enea
A+B(i eae aaeoi?a, o.a. aaeoi?a n ia/aeii a oi/ea
O(0;0) e n eiioeii a oi/ea I(A;B) (?enoiie 2).
Niioaaonoaea onoaiiaeaiiia iaaeaeo iiiaeanoaii eiiieaeniuo /enae, n
iaeiie noi?iiu, e iiiaeanoaaie oi/ae eee aaeoi?ia ieineinoe, n ae?oaie,
iicaieyao eiiieaeniua /enea oi/eaie eee aaeoi?aie.
3.IIAeOEUe EIIIEAENIIAI *ENEA
, o.a.
=A – B(i.
=Z.
, o.a.
(1)
=0 oiaaea e oieueei oiaaea, eiaaea Z=0, o.a. eiaaea A=0 e B=0.
Aeieaaeai, /oi aeey ethaiai eiiieaeniiai /enea Z ni?aaaaeeeau oi?ioeu:
4.NEIAEAIEA E OIIIAEAIEA EIIIEAENIUO *ENAE
Noiiie aeaoo eiiieaeniuo /enae A+B(i e C+D(i iacuaaaony eiiieaeniia
/enei (A+C)+(B+D)(i, o.a. (A+B(i)+(C+D(i)=(A+C)+(B+D)(i
I?iecaaaeaieai aeaoo eiiieaeniuo /enae A+B(i e C+D(i iacuaaaony
eiiieaeniia /enei (A(C-B(D)+(A(D+B(C) (i, o.a.
(A + B(i)((C + D(i)=(A(C – B(D) + (A(D + B(C)(i
Ec oi?ioe auoaeaao, /oi neiaeaiea e oiiiaeaiea iiaeii auiieiyoue ii
i?aaeeai aeaenoaee n iiiai/eaiaie, n/eoay i2= -1. Iia?aoeee neiaeaiey e
oiiiaeaiey eiiieaeniuo /enae iaeaaeatho naienoaaie aeaenoaeoaeueiuo
/enae. Iniiaiua naienoaa:
Ia?aianoeoaeueiia naienoai:
Z1 +Z2=Z2+Z1, Z1(Z2=Z2(Z1
Ni/aoaoaeueiia naienoai:
(Z1+Z2)+Z3=Z1+(Z2+Z3), (Z1(Z2)(Z3=Z1((Z2(Z3)
?ani?aaeaeeoaeueiia naienoai:
Z1((Z2+Z3)=Z1(Z2+Z1(Z3
Aaiiao?e/aneia ecia?aaeaiea noiiu eiiieaeniuo /enae
?enoiie SEQ ?enoiie \* ARABIC 3
Niaeanii ii?aaeaeaieth neiaeaiey aeaoo eiiieaeniuo /enae,
aeaenoaeoaeueiay /anoue noiiu ?aaia noiia aeaenoaeoaeueiuo /anoae
neaaaaiuo, iieiay /anoue noiiu ?aaia noiia iieiuo /anoae neaaaaiuo.
Oi/ii oaeaea ii?aaeaeythony eii?aeeiaou noiiu aaeoi?ia:
Noiia aeaoo aaeoi?ia n eii?aeeiaoaie (A1;B1) e (A2;B2) anoue
aaeoi? n eii?aeeiaoaie (A1+A2;B1+B2). Iiyoiio, /oiau iaeoe aaeoi?,
niioaaonoaothuee noiia eiiieaeniuo /enae Z1 e Z2 ioaeii neiaeeoue
aaeoi?u, niioaaonoaothuea eiiieaeniui /eneai Z1 e Z2.
I?eia? 1: Iaeoe noiio e i?iecaaaeaiea eiiieaeniuo /enae Z1=2 – 3(i e
1 Niinia:
Z2= –7 + 8(i.
Z1 + Z2 = 2 – 7 + (–3 + 8)(i = –5 + 5(i
Z1(Z2 = (2 – 3(i)((–7 + 8(i) = –14 + 16(i + 21(i + 24 = 10 + 37(i
2 Niinia:
5.AU*EOAIEA E AeAEAIEA EIIIEAENIUO *ENAE
Au/eoaiea eiiieaeniuo /enae – yoi iia?aoeey, ia?aoiay neiaeaieth: aeey
ethauo eiiieaeniuo /enae Z1 e Z2 nouanoaoao, e i?eoii oieueei iaeii,
/enei Z, oaeia, /oi:
Z + Z2=Z1
Anee e iaaei /anoyi ?aaainoaa i?eaaaeoue (–Z2) i?ioeaiiieiaeiia /eneo
Z2:
Z+Z2+(-Z2)=Z1+(-Z2), ioeoaea
Z= Z1-Z2
*enei Z=Z1+Z2 iacuaatho ?aciinoueth /enae Z1 e Z2.
Aeaeaiea aaiaeeony eae iia?aoeey, ia?aoiay oiiiaeaieth:
Z(Z2=Z1
?acaeaeea iaa /anoe ia Z2 iieo/ei:
0
Aaiiao?e/aneia ecia?aaeaiea ?aciinoe eiiieaeniuo /enae
?enoiie SEQ ?enoiie \* ARABIC 4
?aciinoe aeaoo eiiieaeniuo /enae Z2 e Z1 ii ii?aaeaeaieth iiaeoey
anoue aeeeia aaeoi?a Z2 – Z1. Iino?iei yoio aaeoi?, eae noiio aaeoi?ia
Z2 e (–Z1) (?enoiie 4). Oaeei ia?acii, iiaeoeue ?aciinoe aeaoo
eiiieaeniuo /enae anoue ?annoiyiea iaaeaeo oi/eaie eiiieaeniie
ieineinoe, eioi?ua niioaaonoaotho yoei /eneai.
Yoi aaaeiia aaiiao?e/aneia enoieeiaaiea iiaeoey ?aciinoe aeaoo
eiiieaeniuo /enae iicaieyao n oniaoii eniieueciaaoue i?inoua
aaiiao?e/aneea oaeou.
Z2 – Z1 = (3 + 4(i) – (4 + 5(i) = –1 – i
6.O?EAIIIIAO?E*ANEAss OI?IA
EIIIEAENIIAI *ENEA
?enoiie SEQ ?enoiie \* ARABIC 5
Caienue eiiieaeniiai /enea Z a aeaea A+ B(i iacuaaaony aeaaa?ae/aneie
oi?iie eiiieaeniiai /enea. Iiieii aeaaa?ae/aneie oi?iu eniieuecothony e
ae?oaea oi?iu caiene eiiieaeniuo /enae.
= r e a?aoiaio ( neaaeothuei ia?acii:
A= r (cos( ; B= r(sin(.
*enei Z iiaeii caienaoue oae:
(sin( = r ((cos(+ i(sin()
Z = r((cos(+ i(sin() (2)
Yoa caienue iacuaaaony o?eaiiiiao?e/aneie oi?iie eiiieaeniiai /enea.
– iiaeoeue eiiieaeniiai /enea.
*enei ( iacuaatho a?aoiaioii eiiieaeniiai /enea.
0 iacuaaaony aaee/eia oaea iaaeaeo iieiaeeoaeueiui iai?aaeaieai
aeaenoaeoaeueiie ine e aaeoi?ii Z, i?e/ai aaee/eia oaea n/eoaaony
iieiaeeoaeueiie, anee ion/ao aaaeaony i?ioea /aniaie no?aeee, e
io?eoeaoaeueiie, anee i?iecaiaeeony ii /aniaie no?aeea.
Aeey /enea Z=0 a?aoiaio ia ii?aaeaeyaony, e oieueei a yoii neo/aa /enei
caaeaaony oieueei naiei iiaeoeai.
Caienue A+ B(i, aaea A e B – aeaenoaeoaeueiua /enea, iacuaaaony
aeaaa?ae/aneie oi?iie yoiai /enea.
, ?aaainoai (2) iiaeii caienaoue a aeaea
sin(, ioeoaea i?e?aaieaay aeaenoaeoaeueiua e iieiua /anoe, iieo/ei:
(3)
Anee sin( iiaeaeeoue ia cos( iieo/ei:
(4)
Yoo oi?ioeo oaeiaiae eniieueciaaoue aeey iaoiaeaeaiey a?aoiaioa (, /ai
oi?ioeu (3). Iaeiaei ia ana cia/aiey (, oaeiaeaoai?ythuea ?aaainoao (4),
yaeythony a?aoiaioaie /enea A + B(i. Iiyoiio i?e iaoiaeaeaiee a?aoiaioa
ioaeii o/anoue, a eaeie /aoaa?oe ?aniieiaeaia oi/ea A + B(i.
7.NAIENOAA IIAeOEss E A?AOIAIOA
EIIIEAENIIAI *ENEA
N iiiiuueth o?eaiiiiao?e/aneie oi?iu oaeiaii iaoiaeeoue i?iecaaaeaiea e
/anoiia eiiieaeniuo /enae.
Ionoue Z1= r1((cos(1 + i(sin(1), Z2= r2((cos(2 + i(sin(2). Oiaaea:
Z1Z2= r1(r2[cos(1(cos(2 – sin(1(sin(2 + i(( sin(1(cos(2 + cos(1(sin(2)]=
= r1(r2[cos((1 + (2) + i(sin((1 + (2)].
Oaeei ia?acii, i?iecaaaeaiea eiiieaeniuo /enae, caienaiiuo a
o?eaiiiiao?e/aneie oi?ia, iiaeii iaoiaeeoue ii oi?ioea:
Z1Z2= r1(r2[cos((1 + (2) + i(sin((1 + (2)] (5)
Ec oi?ioeu (5) neaaeoao, /oi i?e oiiiaeaiee eiiieaeniuo /enae eo iiaeoee
ia?aiiiaeathony, a a?aoiaiou neeaaeuaathony.
Anee Z1=Z2 oi iieo/ei:
Z2=[r(( cos( + i(sin()]2= r2(( cos2( + i(sin2()
Z3=Z2(Z= r2(( cos2( + i(sin2()(r(( cos( + i(sin()=
= r3(( cos3( + i(sin3()
0 e ethaiai iaoo?aeueiiai /enea n ni?aaaaeeeaa oi?ioea:
Zn =[ r(( cos(+ i(sin()]n= rn(( cos n(+ i(sin n(), (6)
eioi?oth iacuaatho oi?ioeie Ioaa?a.
*anoiia aeaoo eiiieaeniuo /enae, caienaiiuo a o?eaiiiiao?e/aneie oi?ia,
iiaeii iaoiaeeoue ii oi?ioea:
[ cos((1 – (2) + i(sin((1 – (2)]. (7)
= cos(– (2) + i(sin(– (2)
Eniieuecoy oi?ioeo 5
(cos(1+ i(sin(1)(( cos(– (2) + i(sin(– (2)) =
cos((1 – (2) + i(sin((1 – (2).
I?eia? 3:
Z3 = – 8
*enei – 8 caieoai a o?eaiiiiao?e/aneie oi?ia
8 = 8(( cos(( + 2(() + i·sin(( + 2(()), (((
Ionoue Z = r((cos( + i(sin(), oiaaea aeaiiia o?aaiaiea caieoaony a
aeaea:
r3((cos3( + i(sin3() = 8(( cos(( + 2(() + i·sin(( + 2(()), (((
Oiaaea 3( =( + 2((, (((
, (((
r3 = 8
r = 2
Neaaeiaaoaeueii:
)), (((
( = 0,1,2…
( = 0
(i
( = 1
)) = 2(( cos( + i·sin() = –2
( = 2
(i
; Z2 = –2
I?eia? 4:
Z4 = 1
*enei 1 caieoai a o?eaiiiiao?e/aneie oi?ia
1 = 1(( cos(2(() + i·sin(2(()), (((
Ionoue Z = r((cos( + i(sin(), oiaaea aeaiiia o?aaiaiea caieoaony a
aeaea:
r4((cos4( + i(sin4() = cos(2(() + i·sin(2(()), (((
4( = 2((, (((
, (((
r4 = 1
r = 1
( = 0,1,2,3…
( = 0
Z1 = cos0+ i(sin0 = 1 + 0 = 1
( = 1
= 0 + i = i
( = 2
Z3 = cos( + i·sin( = –1 + 0 = –1
( = 3
1
i
8.AICAAAeAIEA A NOAIAIUe E ECAEA*AIEA EI?Iss
Ec oi?ioeu 6 aeaeii, /oi aicaaaeaiea eiiieaeniiai /enea r(( cos( +
i(sin() a oeaeoth iieiaeeoaeueioth noaiaiue n iaoo?aeueiui iieacaoaeai
aai iiaeoeue aicaiaeeony a noaiaiue n oai aea iieacaoaeai, a a?aoiaio
oiiiaeaaony ia iieacaoaeue noaiaie.
[ r(( cos( + i(sin()]n= rn(( cos n( + i(sin n()
), anee Zn =(.
0, a, neaaeiaaoaeueii, e Z e ( iiaeii i?aaenoaaeoue a
o?eaiiiiao?e/aneie oi?ia
Z= r(( cos( + i(sin(), (= p(( cos( + i(sin()
O?aaiaiea Zn =( i?eiao aeae:
rn(( cos n( + i(sin n()= p(( cos( + i(sin()
, aaea k((.
Eoae, ana ?aoaiey iiaoo auoue caienaiu neaaeothuei ia?acii:
)], k(( (8)
Oi?ioeo 8 iacuaatho aoi?ie oi?ioeie Ioaa?a.
n oeaio?ii a oi/ea Z = 0.
, neaaeoao iiaeoiaoue i oii, /oiau auei ynii, iiieiaaony iiae yoei
neiaieii ia?a eiiieaeniuo /enae i e -i, eee iaeii, oi eaeia eiaiii.
O?AAIAIEss AUNOEO NOAIAIAE
Oi?ioea 8 ii?aaeaeyao ana ei?ie aeao/eaiiiai o?aaiaiey noaiaie n.
Iaecia?eii neiaeiaa ianoieo aeaei a neo/aa iauaai aeaaa?ae/aneiai
o?aaiaiey noaiaie n:
an(Zn + an–1(Zn–1 +…+ a1(Z1 + a0 = 0 (9)
Aaea an,…, a0 – caaeaiiua eiiieaeniua /enea.
A eo?na aunoae iaoaiaoeee aeieacuaaaony oai?aia Aaonna: eaaeaeia
aeaaa?ae/aneia o?aaiaiea eiaao a iiiaeanoaa eiiieaeniuo /enae ii e?aeiae
ia?a iaeei ei?aiue. Yoa oai?aia auea aeieacaia iaiaoeeei iaoaiaoeeii
Ea?eii Aaonnii a 1779 aiaeo.
Iie?aynue ia oai?aio Aaonna, iiaeii aeieacaoue, /oi eaaay /anoue
o?aaiaiey 9 anaaaea iiaeao auoue i?aaenoaaeaia a aeaea i?iecaaaeaiey:
,
Aaea Z1, Z2,…, ZK – iaeioi?ua ?acee/iua eiiieaeniua /enea, a
a1,a2,…,ak – iaoo?aeueiua /enea, i?e/ai:
a1 + a2 + … + ak = n
Ionthaea neaaeoao, /oi /enea Z1, Z2,…, ZK yaeythony ei?iyie o?aaiaiey
9. I?e yoii aiai?yo, /oi Z1 yaeyaony ei?iai e?aoiinoe a1, Z2 – ei?iai
e?aoiinoe a2 e oae aeaeaa.
Anee oneiaeoueny n/eoaoue ei?aiue o?aaiaiey noieueei ?ac, eaeiaa aai
e?aoiinoue, oi iiaeii noi?ioee?iaaoue oai?aio: eaaeaeia aeaaa?ae/aneia
o?aaiaiea noaiaie n eiaao a iiiaeanoaa eiiieaeniuo /enae ?iaii n ei?iae.
Oai?aia Aaonna e oieueei /oi noi?ioee?iaaiiay oai?aia aeatho ?aoaiey i
nouanoaiaaiee ei?iae, ii ie/aai ia aiai?yo i oii, eae iaeoe yoe ei?ie.
Anee ei?ie ia?aie e aoi?ie noaiaie iiaoo auoue eaaei iaeaeaiu, oi aeey
o?aaiaiee o?aoae e /aoaa?oie noaiaiae oi?ioeu a?iiicaeee, a aeey
o?aaiaiee noaiaie auoa /aoaa?oie oaeeo oi?ioe aiiaua ia nouanoaoao.
Ionoonoaea iauaai iaoiaea ia iaoaao iouneeaaoue ana ei?ie o?aaiaiey.
Aeey ?aoaiey o?aaiaiey n oeaeuie eiyooeoeeaioaie /anoi ieacuaaaony
iieaciie neaaeothuay oai?aia: oeaeua ei?ie ethaiai aeaaa?ae/aneiai
o?aaiaiey n oeaeuie eiyooeoeeaioaie yaeythony aeaeeoaeyie naiaiaeiiai
/eaia.
Aeieaaeai yoo oai?aio:
Ionoue Z = k – oeaeue ei?aiue o?aaiaiey
an(Zn + an–1(Zn–1 +…+ a1(Z1 + a0 = 0
n oeaeuie eiyooeoeeaioaie. Oiaaea
an(kn + an–1(kn–1 +…+ a1(k1 + a0 = 0
a0 = – k(an(kn–1 + an–1(kn–2 +…+ a1)
*enei a neiaeao, i?e naeaeaiiuo i?aaeiieiaeaieyo, i/aaeaeii, oeaeia,
cia/eo k – aeaeeoaeue /enea a0.
9.EAAAe?AOIIA O?AAIAIEA N EIIIEAENIUI IAECAANOIUI
?anniio?ei o?aaiaiea Z2 = a, aaea a – caaeaiiia aeaenoaeoaeueiia /enei,
Z – iaecaanoiia.
Yoi o?aaiaiea:
eiaao iaeei ei?aiue, anee a = 0.
, anee a > 0.
ia eiaao aeaenoaeoaeueiuo ei?iae, anee a
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