Amanani Complex. Ixabiso and Evolution "amanani ngengqondo '

Amanani - izinto ezisisiseko zemathematika ezifunekayo zibalo ezahlukeneyo izibalo. Isethi imilinganiselo zendalo, inani elipheleleyo, esinengqiqo ezingenangqondo digital ichaza nobuninzi ebizwa ngokuba yi-amanani lokwenene. Kodwa kukho kwakhona udidi kakhulu ezingaqhelekanga - ". Izixa ngengqondo 'amanani ezintsonkothileyo kuchaziwe René Descartes njengoko Kwaye enye zezibalo aziintloko kweyeshumi elinesibhozo Leonhard Euler ecetywayo libhekisela kubo le ncwadi i evela French imaginare igama (iplanethi). Yintoni na amanani enzima?

obizwa ngokuba amazwi fom a + bi, apho kwaye b iinombolo yokwenene, yaye i luphawu yedijithali nexabiso okhethekileyo ogama sigcawu -1. Imisebenzi amanani ezintsonkothileyo yenziwa yi imigaqo efanayo njengoko imisebenzi eyahlukeneyo zemathematika kwi polynomials. Olu didi lwezibalo akubonakalisi iziphumo nayiphi na imilinganiselo okanye izibalo. Kuba oku amanani kakhulu ngokwaneleyo lokwenene. Kutheni, ngoko, befuna?

amanani Complex njengengqiqo zemathematika, eyimfuneko ngenxa yokuba ezinye zibalo kunye okuza ngempela baye nezisombululo endle kwamanani "esiqhelekileyo". Ngoko ke, ukuze bandise umda nokungalingani zokusombulula kwavela nemfuno yokuzisa iindidi ezintsha zezibalo. amanani Complex ukuba abstract ikakhulu theoretical kunokwenzeka ukuba ukusombulula ezi zibalo njengoko ² x 1 = 0. Kuyaphawuleka ukuba, nangona ukugcina yayo ibonakale le amanani didi kusetyenziswa ngononophelo kwaye ngokubanzi, umz, ngokuba izisombululo ezahlukeneyo iingxaki theory luthambe, ubunjineli yombane, ezihamba kunye hydromechanics, physics atom kunye nezinye iinkalo zenzululwazi.

Imodyuli impikiswano yenani leqela ezisetyenziswa neeshedyuli zokwakha. Olu hlobo lokubhala ekuthiwa netrigonometri. Ukongeza, utoliko zejometri la amanani iye yandiswa ngakumbi imihlaba zezicelo zabo. Kwazeka lula ukuyisebenzisa kwabo ezahlukeneyo computing mephu.

IMathematika lifikile indlela ende ukusuka amanani elula zendalo iinkqubo ehlanganisiwe kunye nemisebenzi yazo. Kule ndaba uyakwazi ukubhala isifundo esahlukileyo. Apha sijonga nje ezinye iinkalo yendaleko kwethiyori inombolo, yenza kucace zonke izinto zembali yezenzululwazi yangasemva Isizathu sale didi zezibalo.

yezibalo Greek njenge "oyinyaniso" kuphela amanani endalo, nto leyo kusetyenziswa ukubala nantoni na. Sele BC nkulungwane yesibini. e. amaYiputa amandulo kunye amaBhabhiloni ngeendlela ezahlukeneyo izibalo eziluncedo ngokukuko kusetyenziswa amaqhezu. Eli banga elandelayo ebalulekileyo kuphuhliso lwemathematika yaba yimbonakalo amanani akhabayo e-China yamandulo iminyaka engamakhulu amabini ngaphambi kwexesha lethu. Kwakhona esetyenziswa yi sezibalo yamaGrike yamandulo Diophantus, owayeyazi imithetho imisebenzi elula phezu kwabo. Ngoncedo amanani akhabayo, kwaba lula ukuchaza utshintsho ezahlukeneyo imilinganiselo, hayi nje kuphela kweli moya ezintle.

Xa AD Ngenkulungwane yesixhenxe, oko yasekwa ngokucacileyo ukuba iingcambu sikwere amanani akhabayo kusoloko amaxabiso amabini - ukongeza ezintle, nayo negative. Ukusuka yokugqibela yokukhupha ingcambu ka'B nendlela eqhelekileyo aljibra yelo xesha kwakucingwa akunakwenzeka: akukho xabiso enjalo x kwi x ² = ─ 9. Kuba ixesha elide oko akunamsebenzi. Kwaba kuphela kwinkulungwane yeshumi, xa kwakukho kwaye ubesoloko ethatha bafunda quadratic cubic, imfuneko yokukhupha ingcambu ka'B amanani akhabayo, njengoko kwifomula ukuba isisombululo le ntetho iqulethe kuphela ityhubhu, kodwa iingcambu square.

Le ifomyula irobust ezongeziweyo, ukuba equation lusuka kwi ezininzi yangempela. Kwimeko phambi kwesi lenxaki kweengcambu ezintathu ngokwenene okunyanga yabo ifunyenwe kunye nenani engenaxabiso. Kubonakala ukuba indlela yokulungisa apho enqamleza iingcambu ezintathu zingenakwenzeka ngokwembono imathematika yexesha operation.

Ukuze ufumane inkcazelo onesiphumo kephofu algebraists Italian J. Cardano yaphakanyiswa ukwazisa udidi olutsha nohlobo angaqhelekanga amanani, leyo kuthiwa ezintsonkothileyo. Kazi ukuba Cardano ingqalelo kubo luyalambatha wenza konke ukuze siyisebenzisa ndidi zemathematika ecetywayo. Kodwa sele ngo-1572 incwadi Kwabonakala omnye algebraist Italian Bombelli, nto leyo imithetho eneenkcukacha ukuba imisebenzi amanani ezintsonkothileyo.

Kuyo yonke leminyaka elinesixhenxe baqhubeka ingxoxo yohlobo zezibalo manani data kunye izakhono nentsingiselo yawo yemigca. ngcembe nayo yaphuhliswa kwaye nokuphucula ubuchule zokusebenza kunye nabo. Ekuveleni kweyama-17 kunye 18, ithiyori jikelele amanani ezintsonkothileyo zadalwa. Negalelo elikhulu kuphuhliso kunye nokuphuculwa thiyori imisebenzi kweziganga ezintsonkothileyo iye yaziswa Russian kunye izazinzulu Soviet. N. I. Muskhelishvili wenza isicelo yayo kwiingxaki kwithiyori luthambe, Keldysh kunye Lavrentiev amanani ezintsonkothileyo ziye zasetyenziswa kwinkalo osuka kunye ezihamba, kunye Vladimir Bogolyubov - ngokwenkcazo entsimini quantum.